JERUSALEM — When President Trump’s Middle East team meets this week to hash out what to do about Israel’s planned annexation of territory in the West Bank, a fundamental question will hover overhead: Is the prospect of annexation a pressure tactic to get the Palestinians to engage with the administration’s peace plan, or is the peace plan just a smokescreen for annexation?

American and Israeli officials are deeply divided on the question, an issue that could determine how and when any annexation proceeds.

Prime Minister Benjamin Netanyahu has vowed to annex up to 30 percent of the occupied West Bank — as mapped out in the Trump peace plan — as soon as July 1. And he is counting on the Trump administration’s backing, since most of the world views existing Jewish settlements on the West Bank as illegal and would treat any unilateral annexation as a flagrant violation of international law.

But the administration has sent mixed signals, initially greenlighting annexation, then putting the brakes on, and now, apparently, reconsidering the move in White House meetings set to begin on Tuesday.

While both American and Israeli officials support annexation in principle, the White House encouragement came in the context of its plan for resolving the Israeli-Palestinian conflict.

Mr. Netanyahu has distanced himself from some parts of the plan, which also calls for the establishment of a Palestinian state and the freezing of any expansion of Israeli settlements. Those conditions are anathema to the right-wing Israeli settlers whom Mr. Netanyahu sought to woo with annexation in the first place.

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Credit…Ammar Awad/Reuters

The administration has insisted that Mr. Netanyahu obtain the consent of his centrist coalition partner, Defense Minister Benny Gantz, for any annexation. Mr. Gantz, who is on record opposing unilateral annexation, says he will not agree to it without the acquiescence of the king of Jordan. The king, Abdullah II, has warned of a “massive conflict” with Israel if it proceeds.

Mr. Gantz has also insisted that any annexation occur only as an integral part of the Trump administration’s peace plan, which he says he supports in full, not in part.

For anything to happen, someone will have to budge.

“We see the contradictions,” said Ofer Zalzberg, an analyst at the International Crisis Group. “We don’t yet see how they will be resolved.”

Resolving them, Israeli and American officials say, requires resolving a difference of opinion between two close confidants of the president: Jared Kushner, Mr. Trump’s son-in-law and senior adviser, and David M. Friedman, the United States ambassador to Israel, who was Mr. Trump’s longtime bankruptcy lawyer.

Mr. Kushner was lead author of the Trump peace plan, and is said to believe it a viable way to resolve the long-running conflict and potentially reshape the Middle East.

Mr. Friedman, a generous donor to the Israeli settlement enterprise before entering government and who played a key role in reversing a longstanding American policy treating the settlements as illegal, has let it be known that he is more invested in annexation than in the peace plan.

Mr. Kushner’s strategy for getting the Palestinians to engage on the plan involves using the threat of annexation as leverage, officials say. Unilateral annexation would remove that leverage.

For Mr. Friedman, delaying annexation risks missing out on it altogether if Mr. Trump does not win re-election.

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The split between the two surfaced only hours after Mr. Trump, with Mr. Netanyahu beside him, announced his peace plan at the White House in January. Mr. Friedman and Mr. Netanyahu both assured Israeli reporters afterward that Israel was free to annex West Bank land immediately. But Mr. Kushner quickly said that Israel needed to wait, at least until it formed a new government.

Administration officials play down the split and insist the two simply hold different positions on the same team: Mr. Friedman’s brief is limited to Israel and the Palestinians, while Mr. Kushner’s responsibilities include the broader Middle East as well as the Trump re-election campaign.

But Mr. Friedman’s haste, other officials say, aligns him more closely with Mr. Netanyahu and the Israeli ambassador to Washington, Ron Dermer, who are pressing to move quickly on annexation.

Mr. Friedman has effectively dismissed the peace plan as improbable. The conditions the plan imposes on the Palestinians to achieve statehood, he said, are only plausible “when the Palestinians become Canadians.”

Critics have seized on that remark. Yossi Klein Halevi, an author and senior fellow at the Shalom Hartman Institute in Jerusalem, suggested in The Wall Street Journal last week that Mr. Friedman and settler leaders were treating Mr. Trump as a “useful idiot” whose peace plan would serve settler interests now but would never deliver a Palestinian state.

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Even in private meetings, according to Israeli and American officials, Mr. Friedman is asked frequently by Israeli officials whether he is articulating his own views or those of the Trump administration.

Nowhere are the differences between Mr. Friedman and Mr. Kushner clearer, officials say, than over the timing of annexation.

Mr. Netanyahu and his allies are pressing for haste by saying the Trump administration amounts to a “golden opportunity” for American approval that would disappear if Joseph R. Biden Jr., who opposes unilateral annexation, defeats Mr. Trump in November.

But analysts and officials note that this view puts Mr. Friedman in the position of hedging against his boss’s becoming a one-term president.

“It’s wanting to take advantage of what the Trump presidency offers with very low expectations about the Trump presidency,” said Dennis B. Ross, a veteran peace negotiator under Republican and Democratic presidents. “It’s actually quite remarkable.”

Last week, Mr. Friedman tried, and failed, to mediate between Mr. Netanyahu and Mr. Gantz. At one point, officials said, he was kept waiting on a couch for several hours while Mr. Netanyahu and Mr. Gantz haggled over other subjects behind closed doors.

Mr. Friedman’s intervention was widely interpreted in Israel as an attempt to pressure Mr. Gantz.

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The White House discussions on Tuesday are expected to include Mr. Kushner, Mr. Friedman, Secretary of State Mike Pompeo, National Security Adviser Robert C. O’Brien, the Middle East peace envoy, Avi Berkowitz, Vice President Mike Pence and possibly Mr. Trump. According to senior American and Israeli officials, the administration may weigh options including a very limited annexation to win Mr. Gantz’s approval, or letting Mr. Netanyahu go ahead without Mr. Gantz’s agreement, and what the Palestinians could be offered to mollify them.

It also could decide that a unilateral Israeli move, and the resulting furor — including a possible flare-up of violence between Israelis and Palestinians — are unwelcome headaches for a president already facing tumultuous domestic problems and a difficult re-election campaign.

There is also the matter of whether Mr. Netanyahu, if he is denied the green light he has counted on, should be given something else with which to save face back home.

Among the possible inducements for putting annexation on hold, officials said, is reviving an effort to reach a “nonbelligerence” pact between Israel and four Gulf Arab countries: Bahrain, Oman, Qatar and the United Arab Emirates.

Mr. Ross, the former American negotiator, and an official privy to those talks both said that annexation would kill any chance of such a pact. “The message that was conveyed, and I’m not theorizing on this, is annexation means that’s off the table — not just for now, but forever,” Mr. Ross said.

As a political matter, annexation is seen as of limited value to Mr. Trump. The evangelical Christian world, a vital segment of his base, is mostly indifferent to annexation by itself, said Robert Jeffress, pastor of First Baptist Dallas and one of Mr. Trump’s informal evangelical advisers.

Joel C. Rosenberg, an evangelical author who founded a group that mobilizes Christians to support Israel, warned that if annexation creates turmoil it could backfire against Mr. Trump. “I don’t see any pickup among evangelical voters for this move, and there’s a risk that you could lose some evangelical votes, in the very states where you might be more vulnerable,” he said.

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Credit…Samar Hazboun for The New York Times

Officials were loath to make any predictions about where the discussions might end up, particularly given the president’s unpredictability. “If Trump doesn’t see a big electoral benefit, he might just say, ‘Too messy, too complicated, I’ll deal with it if I’m re-elected,’” said David Makovsky, a former peace negotiator now at the Washington Institute for Near East Policy.

Mr. Netanyahu’s dual messaging has embodied the split over what annexation represents.

In Israel, he and his closest allies insist that two pillars of the Trump plan — a Palestinian state and a four-year freeze of construction in the settlements — are not in the offing.

But Mr. Netanyahu’s ambassador to the United States, Mr. Dermer, wrote in The Washington Post on Saturday that annexation would “open the door to a realistic two-state solution” under the Trump plan.

Another Netanyahu confidant, the lawmaker Tzachi Hanegbi, said the key word was “realistic.”

“We don’t care if you call it a state-minus or autonomy-plus, as long as you understand that it’s not really sovereign,” Mr. Hanegbi said.

But Mr. Ross suggested that Mr. Kushner might draw a different conclusion. “What it probably says to Jared is, ‘For Bibi and company right now, this is just an annexation plan,’” he said, using Mr. Netanyahu’s nickname. “‘And that’s not what we put out.’”

Elizabeth Dias contributed reporting from Washington, and Adam Rasgon from Tel Aviv.