A few hours before President Obama offered his historic endorsement of same-sex marriage on Wednesday, Vice President Joseph R. Biden Jr. apologized to the president in the Oval Office for forcing Mr. Obama’s hand by airing his own views three days earlier, several people briefed on the exchange said on Thursday…

Mr. Obama, in an interview with ABC News, said the vice president had gotten “a little bit over his skis” but had done so “out of generosity of spirit.” The president bore Mr. Biden no lingering ill will, according to several officials, though the episode enraged Mr. Obama’s senior advisers in the White House and on the campaign.