WASHINGTON — President Joe Biden is on a public and private blitz to shake off concerns about his cognitive capacities.

But with public doubts about his fitness to serve unabating, Biden’s every move is now under a withering microscope as any potential stumble risks becoming magnified and delivering another blow to his candidacy.

To wit: As he introduced Ukrainian President Volodymyr Zelenskyy at a NATO summit event Thursday, Biden flubbed and called him “President Putin,” prompting gasps from the audience. He corrected himself, saying, “I’m so focused on beating Putin” before ceding the lectern.

Shortly after, at a news conference, Biden errantly referred to “Vice President Trump” — a gaffe that overshadowed what his aides felt was otherwise a commanding performance.

And a significantly hyped recent interview with ABC’s George Stephanopoulos was meant to show Biden could handle scrutinizing questions from the media but only flared more concerns from Democrats about whether he could continue to serve as the party’s nominee.

“If you are going to raise the stakes on one interview, it can’t be another example of you being hard to understand — not because he’s soft, not because he’s mumbling, but because his train of thought doesn’t make sense,” former Obama White House aide Jon Lovett said on his podcast, “Pod Save America,” referring to the Stephanopoulos interview.

Still, getting Biden out there in more unscripted settings has been one consistent plea from Democrats who were rattled by his 90-minute debate June 27 and are seeking assurances that the performance was an unusual blip and not a sign of broader mental decline.

They want to see the glad- handing, the lengthy exchanges with journalists that had been characteristic of Biden, particularly during his 36 years in the Senate.

He’s hopscotched from one event to another since: chatting up supporters at a Detroit restaurant; rallying voters in Wisconsin; stopping at a coffee shop in Harrisburg, Pennsylvania; taking some questions from donors, lawmakers and mayors in private virtual calls. He’s hosted Democratic governors at the White House while picking up his pace of news interviews, including with Stephanopoulos, the Houston Chronicle and NBC News, which will air Monday.

“There’s a number of us that since before the debate were encouraging the campaign, pushing the campaign to let Joe be Joe,” said Sen. Alex Padilla, D- Calif., one of the lawmakers who spoke privately with Biden following his disastrous debate with Donald Trump.

Yet some of his recent outings and meetings have left puzzling results.

During an interview with WURD radio in Philadelphia, Biden tripped up and said, “I’m proud to be, as I said, the first vice president, the first Black woman to serve with a Black president” — scrambling some of his often-used lines about his pride in serving with the first Black president and choosing the first Black woman to be vice president.

The slip came even after it was revealed that the interviewer had asked questions specifically offered up by the Biden campaign.

By no means has Biden been known as an error-proof politician during his decades in public life; rather, his gregarious political style has often been marked by verbal gaffes.

But having Biden be out there more is a risk that his advisers are gambling is worth taking.

“Joe Biden has been making gaffes for 40 years. He made a couple last night. He’ll probably continue to do so,” Michael Tyler, the Biden campaign’s communications director, said on Air Force One as the president traveled Friday to Detroit.

“Our opponent is somebody who every single day out on the stump is calling for a bloodbath if he loses, who’s pleading to rule as a dictator on day one, and who’s pledging to ban abortion nationwide across the country,” Tyler said.

Biden’s allies and aides contend that his direct engagement since the debate — whether it’s voters in unscripted stops during his travels or with scores of mayors from across the country, none of whom voiced concerns about his fitness for office — have proven that the president is still up for the job.

On a call with mayors Wednesday, Lansing, Michigan, Mayor Andy Schor noted that although many mayors had their hands raised on the Zoom call, Phoenix Mayor Kate Gallego ended the session after taking only three questions.

Still, Schor noted that Biden was “rattling off thing after thing,” all what mayors wanted to hear, and “he wasn’t really doing it with notes.”

Sen. Chris Murphy, D- Conn., has also stressed that Biden must do more to convince voters that his debate performance was a one-off.

“I don’t think he or the campaign should be reticent at all in directly engaging with voters or the media in an unscripted way,” he said. “Joe Biden’s occasional gaffes have, in part, been what has made him so endearing and so popular because he’s willing to talk in an authentic, off-the-cuff manner that a lot of politicians aren’t willing to do.”

During Biden’s rally in Madison, Lisa Gellings and her son, Tim, were in an overflow room watching his remarks. Then the president popped in for a surprise visit.

“He isn’t the best on TV,” he said. “He’s much better like this, talking to us.”