President Trump has always stood ready to tear down his immediate predecessors, lobbing deeply personal insults and offering unfavorable interpretations of former presidents Joseph R. Biden Jr. and Barack Obama.

But in recent months, he has been reaching further back into American history, either attaching himself to the achievements of past presidents or insisting he would never replicate their failures.

Mr. Trump is “a one-man Sousa Band of trying to put down other presidents or attach himself to the greatness of George Washington or Theodore Roosevelt or Andrew Jackson,” said Douglas Brinkley, a presidential historian at Rice University.

The New York Times compiled some of Mr. Trump’s comments on 10 past presidents, offering a glimpse into how he sees himself in the context of history.

16th President

Abraham Lincoln

The people that make the biggest impact, they’re the ones that they go after.

Said at an April 25 news conference at the White House.

After a gunman tried to break into the White House Correspondents Dinner in an apparent attempt to assassinate Mr. Trump, a reporter asked the president why this kept happening to him. It was the third time someone tried to kill him.

Mr. Trump named Lincoln, who unified the North and South after the Civil War and was then shot and killed by Confederate sympathizer, to suggest he was in good company.

“I hate to say I’m honored by that,” he added, “but I’ve done a lot.”

That was always the one I didn’t want to be.

Said at a June 17 news conference announcing the framework of a deal with Iran.

The war with Iran inflated energy costs for Americans, jeopardizing Mr. Trump’s promise to address the affordability crisis.

When announcing the framework for a deal with Iran, Mr. Trump suggested he had pushed toward a resolution “rather than possibly going into a depression, rather than having your favorite president be Herbert Hoover.”

Mr. Trump accused him of causing the Great Depression, but historians generally don’t agree — Hoover was less than eight months into his presidency in October of 1929 when the stock market crashed. But he became increasingly unpopular for failing to address the economic turmoil head on and was voted out in favor of Franklin D. Roosevelt.

By his own admission, Mr. Trump was concerned about his economic legacy. Presidencies are often shaped by how voters feel about the economy, and Americans have consistently named the economy as their top concern as the country nears midterm elections.

He had our American flag planted on every part of the world.

Said on July 1 at the opening of the Theodore Roosevelt Presidential Library.

Mr. Trump was filled with praise for Roosevelt. But rather than dwell on his progressive domestic achievements that built out the federal government, Mr. Trump seems to see his own obsession with how America is perceived internationally as an extension of Roosevelt’s leadership, which coincided with the rise of the United States as a global power.

The magnitude of Roosevelt’s domestic accomplishments may have led to his likeness being carved into Mount Rushmore, but Mr. Trump’s approach to American power, which has included proposing to annexing Canada, Mexico, Greenland and even Venezuela, diverges.

Mr. Trump appeared to be reaching into “a grab bag of history” and missing the nuances, said Tim Naftali, a presidential historian at Columbia University. Roosevelt didn’t plant the flag around the globe, Mr. Naftali said, though he did force negotiations for the United States to take the land of the Panama Canal Zone. (The Canal Zone ceased being U.S. territory in 1979 and Mr. Trump has often said he wants it back.)

They call it the ‘Donroe.’

Said in a Jan. 8 interview with Fox News host Sean Hannity.

Days after the U.S. military successfully dropped into Venezuela and extracted its president, Nicolás Maduro, Mr. Trump hinted that he might lead the United States to intervene in other international arenas.

Mr. Trump was asked whether he was calling that strategy the “Donroe Doctrine,” after James Monroe’s 1823 unilateral declaration of American power and interest in the Western Hemisphere that was eventually used to justify U.S. intervention in Latin America. But he shied from the title that some supporters had tossed around.

“I didn’t call it that,” he said, “but they’re calling it this.”

Mr. Trump, who has called the declaration Monroe’s “claim to fame,” then launched a war on Iran, wading into the possibility that his legacy would be shaped by the foreign conflicts that he campaigned against. But the war also re-established the United States as an interventionist military power.

“He wants his legacy to be that he was a key power,” Mr. Brinkley said.

Andrew Jackson was treated horribly.

Said on Jan. 6, before Republican members of the House.

Five years to the day his supporters attacked the U.S. Capitol, Mr. Trump seemed to see in Jackson a fellow sufferer.

Mr. Trump was impeached a second time for inciting that mob with a speech refusing to concede the election he had just lost to Joseph R. Biden Jr. Over the years he has made it clear he begrudges his treatment by Congress.

He begrudges Jackson’s treatment, too. Still, “he never got impeached twice,” Mr. Trump said. In fact, Jackson was never impeached, only censured by Congress.

“I got impeached twice over nothing.”

What a mess.

Said on March 9 at a Republican conference.

The pitfall of Carter’s presidency was the Iran hostage crisis, the 444 day standoff over 52 Americans taken captive by militants from the U.S. Embassy in Tehran.

Several weeks into what Mr. Trump had told Americans would be a short conflict with Iran, Carter’s biggest political blunder was evidently on his mind.

“Look at what happened with the helicopters and the hostages,” Mr. Trump said. “It cost them the election.”

40th president

Ronald Reagan

I thought he was great, great style and everything.

Said in an interview in Beijing with Fox News Host Sean Hannity, aired May 14.

“But he was not good on trade,” Mr. Trump quickly added.

Mr. Trump has previously compared his own political movement to that of Reagan, the popular Republican president whose policies are still held up as an example by modern conservatives.

Mr. Trump sees himself as an icon of the American right, as Reagan has become. But he doesn’t appear to share an interest in Reagan’s traditional conservatism and has turned the Republican Party toward his own right-wing populism.

Still, Mr. Trump seems happy to lean on Reagan’s popularity, once sharing on social media a fake quote in which Reagan praised a young Mr. Trump.

37th president

Richard Nixon

I wouldn’t have preferred Nixon.

Said at a June 17 news conference announcing the framework of a deal with Iran.

In the same breath that he said he did not want to make economic missteps akin to Herbert Hoover’s, Mr. Trump added that he would not want to be the president behind Watergate, perhaps the most consequential political corruption scandal to embroil a sitting U.S. president.

Mr. Trump knows the scandal well, saying he learned from it not to repeat the firings of Nixon’s Saturday Night Massacre, or to tape incriminating conversations.

But perhaps the biggest lesson was not to give up office. Though Nixon resigned while facing almost certain impeachment and removal, Mr. Trump seems to have seen it as a decision to accept defeat.

“He left. I don’t leave,” Trump once said of Nixon. “Big difference. I don’t leave.”

39th president

William McKinley

He was the tariff king.

Said on July 1 at the opening of the Theodore Roosevelt Presidential Library.

At the event honoring Theodore Roosevelt, Mr. Trump digressed on a president about whom he had often spoke positively.

McKinley was a proponent of economic policies that today might be seen as Trumpian. He also notched some victories that Trump seems to have designed for his own legacy, including installing protectionist tariffs. They did not, as Mr. Trump suggested, make the country “tremendous amounts of money,” something Mr. Trump also vowed his tariffs would do.

Still, tariffs are part of McKinley’s legacy — something Mr. Trump hasn’t been able to replicate. It was one of several big efforts of Mr. Trump’s second term that didn’t stick.

“The Supreme Court said, ‘You went too far,’” Mr. Naftali said.

1st president

George Washington

The city named in honor of General George Washington.

Said on June 24 at the exposition on the National Mall in honor of America’s 250th birthday.

To a brand-obsessed businessman like Mr. Trump, George Washington’s greatest legacy is perhaps all that is named after him.

In his second term, Mr. Trump has become preoccupied with renovation and building projects at the White House and across the capital, dotted with buildings and monuments named for celebrated American presidents.

Mr. Trump, a real estate developer known for naming his projects after himself, has launched an effort to leave his imprint on many of those American icons and even construct new ones.

“His building program in the second term is clearly a sign of his focus on legacy,” Mr. Naftali said.

“He wants his own Washington.”