The Republican candidate had been a
leader of the "birther" movement that questioned Hawaii-born Mr
Obama's citizenship.
But his campaign now accuses his
Democratic rival Hillary Clinton of introducing the "smear" during
the 2008 Democratic nomination contest.
There is no evidence to link Mrs
Clinton to the birthers.
In reaction she tweeted that
President Obama's successor "cannot and will not be the man who led the
racist birther movement".
Does it matter where a country's
leader is born?
The BBC's North America Reporter
Anthony Zurcher says the statement signed by senior Trump advisor Jason Miller
is far from an admission of error.
Instead, he says, Mr Miller laid the
genesis of the birther rumours wrongfully at the feet of Hillary Clinton and
her 2008 presidential campaign team.
When they raised questions, Mr
Miller said, it was "vicious and conniving" behaviour. By broaching
the topic three years later, Mr Trump had done a "great service" to
the public and president, Mr Miller said.
The statement follows an interview
with the Washington Post newspaper in which Mr Trump had declined to say Mr
Obama had been born in the US, saying instead that he did not want to answer
the question.
What
is the origin of the 'birther' claim?
The claim is a conspiracy theory
that Mr Obama was actually born in Kenya and is therefore ineligible to be
president.
Reports in various US publications
suggest it was circulated in 2008 by die-hard supporters of Mrs Clinton as it
became clear that she was not going to win the Democratic nomination.
However there is no evidence that
Mrs Clinton or her then campaign had anything to do with it.
The claim enjoyed a revival with
some supporters of Republican candidate John McCain as he fell behind Mr Obama
in polls, the Fact Check website reported.
The billionaire became a vocal
questioner of Mr Obama's citizenship as he was running for a second term as
president.
In April 2011, Mr Trump challenged
Mr Obama to show his birth certificate, gaining approval from Republicans
including former Alaska governor Sarah Palin.
Weeks later Mr Obama released his
actual birth certificate from his native state of Hawaii. At that year's White
House correspondents dinner, Mr Obama made light of the allegations, mocking
Donald Trump.
The 2012 Republican candidate Mitt
Romney referred to the discredited theory at a campaign rally in August that
year, joking that no-one had asked to see his birth certificate - drawing swift
condemnation from the Obama campaign.
Why
has the Trump campaign now distanced itself?
The words haven't been spoken by
Donald Trump yet, but a press release from his campaign represents the closest
we've come to the Republican nominee formally acknowledging that President
Barack Obama was born on US soil.
Mr Trump's turn as the lead advocate
of the so-called "birther" movement has been a drag on the
Republican's standings among black voters. It was also the issue that rocketed
the New Yorker to fame among many conservatives, however.
There's little surprise, then, that
Trump team wants to settle the matter and shift the campaign back to more
favourable terrain - but the candidate has yet to back down completely.
What
is the latest on the campaign?
- Mr Trump's doctor has said he is in excellent physical health, although Mr Trump said he was slightly overweight.
- Mrs Clinton has returned to the campaign train after three days off with pneumonia.