Donald Trump has long attacked Joe Biden, his likely opponent at the polls next year, as “Sleepy Joe”, portraying the 80-year-old president as too old and too mentally fogged to occupy the Oval Office. As recently as Friday, the former president attacked his successor for being unfit to deal with Russia and the threat of nuclear war.

But Trump’s tactics rebounded when he said Biden threatened to lead the US into “world war two” – and suggested that he, Trump, thought he had beaten Barack Obama for the presidency back in 2016.

There have been two world wars. The first ended in 1918, the second in 1945. The cold war, the nuclear stand-off between the US and the Soviet Union that often threatened a third world war, ended with the fall of the communist regime in Moscow in 1991.

Obama was president, and Biden vice-president, from 2009 to 2017. In the 2016 election, Trump beat Hillary Clinton.

Mockery of Trump’s stumbles was immediate and sustained. But it also pointed to an increasingly stark issue on both sides of the aisle: the advanced age of many American leaders, and polling that shows most voters want generational change.

At 80, Biden is the oldest president ever. Should he win re-election and serve a full term, he will be 86 on leaving office. Polling has shown more than 75% of Americans think he is too old for a second term.

Trump is 77 but polls show significantly fewer voters think he is too old to return to power. Whether gaffes like those he made in Washington move the needle remains, of course, to be seen.

Addressing the Pray, Vote, Stand summit, a rightwing event, Trump said Biden was “cognitively impaired, in no condition to lead and … now in charge of dealing with Russia and possible nuclear war”.

Under Biden, he added: “We would be in world war two.”

On Monday, the MSNBC host Joe Scarborough, a former Republican congressman, laughed as he said: “It’s almost like it’s the summer of 1939 all over again. You know, [Trump’s] father’s going to a Nazi rally or something, or a Klan rally. I don’t know which rally he did or didn’t go to.”

Trump’s father, Fred Trump, was arrested after a Klan riot in Queens, New York, in 1927. Donald Trump has reportedly expressed sympathy for Nazism and Adolf Hitler.

“But yeah,” Scarborough said. “You think they may want to take out the ‘cognitively impaired’ part of his speeches from now on.”

Jonathan Lemire, his fellow host, said: “That’s an attack line the Republicans and Trump love to use [against Biden] but, man, that does seem like he was looking in the mirror just there.

“I mean … we see these polls that suggest that voters are more concerned about President Biden’s age than Donald Trump’s age. Trump is only three years younger and anyone watching Trump day in, day out says he’s changed too.”

Biden says he is fit to serve. So does Trump, telling NBC in an interview broadcast on Sunday “there should be a competency” test for presidents, of the sort he “aced” while in the White House. That prompted memories of previous national mirth, when in summer 2020 Trump, then 74, bragged about successfully recognising “person, woman, man, camera, TV” in a cognitive exam.

But, again, the issue remains a serious one.

Democrats protest that disproportionate attention is paid to Biden’s age than that of Trump. Last week, Chuck Rocha, a Democratic strategist, told CBS News: “Joe Biden is getting older, we all know that. But the other guy he’s probably going to be running against is getting older, too. And in the focus groups that I’m doing, old and steady still beats old and crazy.”

Nonetheless, on Sunday, a new poll from CBS and YouGov said only 34% of voters thought Biden would complete a second term if elected. Asked the same question about Trump, 55% said they thought he would complete a full four years.

Asked if the two men had the necessary mental and cognitive health to be president, 26% said only Biden did, 44% said only Trump did and 23% said neither did.

Ninety-one criminal charges and assorted civil lawsuits notwithstanding, Trump leads Republican polling by wide margins. His challengers have made age and cognitive ability an issue but such is Trump’s dominance, they have mostly directed their fire at Biden.

Ron DeSantis, the hard-right Florida governor who is a distant second to Trump, said last week age was “absolutely a legitimate concern” when electing a president.

“The presidency’s not a job for someone that’s 80 years old,” DeSantis told CBS.

He did not say if he thought the same about someone who was 77, and who the former Republican party chair Michael Steele called a “dumbass”, over his Washington remarks.

But DeSantis added: “Obviously, I’m the governor of Florida, I know a lot of people who are elderly, they’re great people, but you’re talking about a job where you need to give it 100%, we need an energetic president.”

Concern about the age of many US party leaders has spread beyond the presidency, particularly given public health scares suffered by Mitch McConnell, the 81-year-old Republican leader in the Senate, and Dianne Feinstein, the 90-year-old Democratic senator from California.

DeSantis said: “I think that if the founders could kind of look at this again, I do think they probably would’ve put an age limit on some of these offices.”