The Trump campaign has acknowledged in a statement that President Obama was born in the US.
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.