President Biden said Friday that while he has not made a formal decision about running for reelection in 2024, he intends to do so - citing previous encouragement from his late son, Beau, and revealing that he has the backing of his wife, first lady Jill Biden.

In an interview that aired Friday, MSNBC's Jonathan Capehart quoted Biden's 2017 autobiography, "Promise Me, Dad," in which the president wrote that Beau had insisted he run for the office in 2016, saying that his father had a duty to do so. Capehart asked what words Beau - who died of brain cancer in 2015 - would have for those who say Biden should not run again because of his age.

"The only reason to be involved in public life is: Can you make life better for other people?" Biden answered. "Depending on who the opponent is, if they have a view that is so the antithesis of what I believe democracy [is], and I believe is good for average Americans, then, his argument was, 'Dad, you have an obligation to do something.' "

When asked if the first lady supports a 2024 run, Biden nodded and paused before providing a full answer. "My wife thinks that we're doing something very important and that I shouldn't walk away from it," he said.

But Biden said he was not yet formally declaring his candidacy, because once he does, a "whole series of regulations kick in, and I have to treat myself as a candidate from that moment on.

"I have not made that formal decision, but it's my intention. My intention to run again. And we have time to make that decision," he said.

The 79-year-old - who was the oldest person to be sworn into office - has faced questions from his own party about whether he should seek reelection, due to his age and low approval ratings. Biden has sought to downplay the doubts by engaging in public displays of outdoor activities and indicating multiple times he will run again since last year.

In June, White House spokeswoman Karine Jean-Pierre said that he plans to run in 2024. This month, NBC reported that Biden had told Rev. Al Sharpton he would seek another term.

But the president's best argument for another bid has been the reemergence of former president Donald Trump. Biden was motivated to run for office in large part because he saw himself as best positioned to defeat Trump, and he still considers knocking Trump out of the White House one of his major contributions to the United States' welfare, The Washington Post reported.

Trump has vowed to pardon rioters who stormed the U.S. Capitol on Jan. 6, 2021, and has maintained his false claims of fraud in the 2020 election, known as the "big lie." Meanwhile, Biden has increasingly voiced concerns over what he called an "assault on American democracy."

"We are still at our core a democracy - yet history tells us that blind loyalty to a single leader, and the willingness to engage in political violence, is fatal to democracy," Biden said last month. "There is no question that the Republican Party is dominated, driven and intimidated by Donald Trump."

In August, the president accused Trump of harboring an "extreme MAGA philosophy," likening it to "semi-fascism." The lines were unplanned, aides said.

In Friday's MSNBC interview, the president repeated the message. There "has been such a division . . . you have what I call the 'mega MAGA Republicans,' " he said. They "think it's all right to threaten violence, think that's not inappropriate, talk about how they're concerned about security, but yet you saw what happened on January 6th," he said.

But a Washington Post-ABC poll from last month indicates that a Biden-Trump rematch wouldn't be the preferred slate for many Americans: 56 percent of respondents leaning toward the Democratic Party said they'd prefer a nomination for "someone other than Biden," while 47 percent of those leaning Republican said they'd want Trump - down from 67 percent in October 2019.

The Washington Post's Matt Viser contributed to this report.