COLUMBUS, Ohio — The 2016 presidential campaign has followed a pattern: In a contest featuring two widely disliked candidates, each has risen in response to the other's failings and each has fallen due to self-inflicted wounds.

Hillary Clinton rose in polls late this summer after Donald Trump's undisciplined attacks on a Gold Star family and other remarks that insulted racial or ethnic minorities pushed away centrist voters.

Trump more recently has risen on concerns about Clinton's family foundation, her comment that half of his voters belonged in “a basket of deplorables” and her reluctance to be fully transparent about her health.

Just when he might have sought to cement and extend his new, narrow lead in some swing states, Trump on Friday delved into a topic the GOP presidential nominee recently had tried to avoid — his long effort to prove President Barack Obama is not an American citizen. And he did so by making fresh and demonstrably inaccurate accusations against his Democratic rival.

Trump's problem is that to gain a foothold on the Republican electorate he adopted a false claim — that Obama was not born in the United States and was, therefore, an illegitimate president. And he doggedly stuck to that assertion for five years.

But the accusation appeals to far fewer voters than a candidate needs to win the White House. So Trump's advisers — if not the candidate himself — have eagerly looked for a way he could climb down.

Nothing Trump said Friday will loosen the grasp of his fervent supporters, who indicate they are less concerned about what Trump says than their belief that he's speaking for them.

The voters who haven't yet chosen sides, however, indicate they want more — including details about how he would govern.

The impact of Trump's latest statements cannot be measured immediately. But if his point was to appeal to those voters by putting his birther campaign behind him, he will not be helped by the endless loop of television clips showing him casting doubt on an increasingly popular president.

But for Trump's own actions, those voters might have been hearing Friday about the economic plan he had released the day before or the child care proposals he made earlier this week. Instead, they were reliving a fight that started five years ago.

Trump's terse comments, and his erroneous statements about Clinton, followed events in which he behaved more like the old Trump who had worried suburban and less-partisan voters in whose hands the election increasingly seems to rest.

He refused to concede Obama's birthplace in a Washington Post interview published Thursday. He claimed Friday morning that he couldn't tell Fox broadcaster Maria Bartiromo what he believed because “we have to keep the suspense going”— as though stoking interest in a coming reality show.

Later Friday, at the close of an event in Washington that also served to promote his new hotel, Trump falsely claimed that Clinton and her 2008 presidential campaign “started the birther controversy” and that he had “finished it.”

There is no evidence that Clinton or her campaign ever circulated the idea that Obama had not been born in the U.S., although some individual supporters of hers made that claim late in the 2008 primary season.

Trump then said that Obama “was born in the United States, period.”

He offered no apology for doubting the president's legitimacy. He also did not explain what had caused him to change his mind, since no new facts have emerged in the years he has been suggesting Obama was born in Africa — a claim he had repeated in interviews as recently as 2014, long after Obama released his birth certificate.

For both candidates this year, a big part of the campaign has been about convincing voters to overlook — or forgive — their flaws.

For Clinton, that means getting voters past fears about her trustworthiness.

She has offered reams of policy proposals, but since much of the campaign this year has focused on Trump she has had a hard time getting out her own message.

Instead, high-profile embarrassments have put out a message she does not want to circulate.

In the case of her recent bout with pneumonia, her supporters worry that not disclosing an illness until video surfaced of a near-collapse would further the perception of dishonesty.

In Trump's case, his campaign has been about persuading voters to disregard his showman instincts and sometimes-coarse manner and instead seize on him as a transformative figure ready to punish the purveyors of politics as usual.

But as a result of his own actions, the voters he needs are now being hit with the reminders of Trump advocating a fringe belief about Obama.

cathleen.decker@latimes.com