The authorities know that a statue of the renowned Black abolitionist Frederick Douglass was torn from its base in a park in Rochester, N.Y., and then dumped some 50 feet away, where it was discovered near a river gorge.

The statue was found on Sunday, July 5, the 168th anniversary of one of Douglass’s most famousspeeches denouncing slavery, and the damage was done amid a heated national debate over tributes to historical figures.

But in the two days since the Rochester police began their investigation, and as prominent leaders have linked the destruction to a variety of ideological motivations, it was still unclear who vandalized the statue or why.

Nor do the authorities know whether the historically noteworthy timing was intentional or merely coincidence.

“We’re still looking into it,” Jacqueline Shuman, a police spokeswoman, said. “We don’t have anything that suggests that it’s related to any of that.”

Still, without any clear answers, the news of the statue’s destruction set off wide speculation about whether it was connected in some way to the continuing debate over the defacement, toppling and removal of monuments honoring Confederate generals and other controversial white historical figures.

On Monday, President Trump weighed in. In speeches over the July Fourth weekend, he had portrayed the destruction of national monuments as an assault on American values. He said on Twitter that the vandalism in Rochester was the work of “anarchists,” a term he has used repeatedly to describe protesters marching against police brutality. Some protesters have also urged, and some have carried out, the removal of statues of pro-slavery figures.

The Rochester police said they had not found anything to confirm or debunk a link to “anarchists,” a connection that was made more explicitly by the president’s son Donald Trump Jr. and Representative Lee M. Zeldin, a Long Island Republican. Both men have invoked Marxism as the driving philosophy behind the country’s anti-racism movement.

“When I saw that tweet, I was like, ‘Oh boy,’” Ms. Shuman, the police spokeswoman, said of the president’s comment. “Especially given the current climate and everything that’s going on.”

The police also do not have enough evidence to affirm or negate an alternate theory proposed by some people, including Cornell William Brooks, a former president of the N.A.A.C.P.: that the vandalism had been carried out by white supremacists seeking vengeance for destructive acts against Confederate monuments.

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Credit…Tina Macintyre-Yee/Democrat & Chronicle, via Associated Press

The statue of Douglass that was vandalized was erected in Maplewood Park in 2018, one of 13 of the famed orator placed around Rochester that year to commemorate the 200th anniversary of his birth.

Douglass, who escaped slavery in 1838 and went on to become one of its most well-known opponents, lived in Rochester for more than two decades. He published his abolitionist newspaper, The North Star, there, and he was buried in the city after his death in 1895.

He also gave his famed “What to the Slave Is the Fourth of July?” speech there on July 5, 1852. In the address, he said that the United States could not genuinely celebrate its commitment to liberty and independence while enslaving and oppressing Black people.

The text of the speech was shared widely on social media over the weekend, its message given resonance amid a newly prominent movement to address institutional racism that was inspired by the killing in police custody of George Floyd in Minneapolis.

Carvin Eison, who led the project that brought the Douglass statues to Rochester, said the historical significance of the date when the vandalism was discovered could not be ignored.

“Once you make that connection, you realize that it is impossible to disconnect the damage and the removal of the statue from the date of the address,” Mr. Eison said. “All kinds of theories and conspiracies go through your head.”

Mr. Eison said that he could not know what motivated the vandalism, but he added that he thought it was unlikely that the Douglass statue was toppled by someone who was upset about monuments honoring Confederate figures. Douglass clearly stood in direct opposition to those men.

Mr. Eison also said he did not discount that there might be a link to the debate over Confederate tributes.

“If this monument was destroyed, it’s only logical that it was some kind of retaliation event in someone’s mind,” he said.

He added that he was especially dispirited by the statue’s destruction because of its location near Kelsey’s Landing, a point along the Underground Railroad where Douglass and others helped escort enslaved people to freedom.

Rochester’s mayor, Lovely A. Warren, also said the statue’s location made its destruction particularly upsetting.

“To have any Frederick Douglass statue damaged in our city of course is disheartening,” Ms. Warren said in an interview. “But the significance of that particular statue and the place where it marked? It’s is a travesty and a devastation.”

It was not first such act of vandalism in Rochester. In December 2018, two white college students were charged with damaging and attempting to steal a different statue of Douglass. Both men later pleaded guilty, saying that they had been drunk and that their actions were not racially motivated.

Mr. Trump has invoked Douglass’s name before.

At a Black History Month event at the White House in 2017, the president cited him as “an example of somebody who’s done an amazing job and is being recognized more and more.” The remark caused some of Mr. Trump’s critics to question whether he knew Douglass was dead.

Ms. Warren, a Democrat, said she did not know who removed the statue from Maplewood Park and she declined to offer a potential motive. But she criticized Mr. Trump’s speculative tweet as divisive and she suggested that his past use of inflammatory language about race made his message insincere.

“Regardless of who did it, the significance of Frederick Douglass matters,” Ms. Warren said. “My message in all of this is that you will not destroy the legacy of this man.”