Washington ? Barack Obama and Hillary Rodham Clinton sat in comfortable chairs, sipped water and spoke for an hour about the presidential campaign to come. Just the two of them, without aides. And they parted laughing.

Aside from a fleeting backstage encounter in between their respective speeches to a pro-Israel group Wednesday, this was the first face-to-face meeting between Obama and Clinton since he clinched the Democratic presidential nomination and she moved to end her bid and endorse his candidacy.

Neither Obama or Clinton have disclosed details of this meeting Thursday night at the home of a Senate colleague, Democrat Dianne Feinstein.

But Feinstein told reporters Friday that Clinton called her Thursday afternoon and asked if she and Obama could meet at the California senator’s home. The two former rivals arrived and left separately, Feinstein said, and had no staff in the room with them as they talked. Feinstein showed them into her living room at 8 p.m. CDT, then left them alone and went upstairs to do her own work.

“There was a desire on both sides, I think, to have a private meeting,” Feinstein said Friday.

“They called me when it was over,” Feinstein said. “I came down and said, ‘Good night everybody, I hope you had a good meeting.’ They were laughing, and that was it.”

Clinton’s campaign said she would deliver her formal endorsement of Obama today during a noon gathering at the National Building Museum and would urge Democrats to unite behind his candidacy. Obama secured the 2,118 delegates needed to win the nomination Tuesday after primaries in Montana and South Dakota.

At home in Chicago for the weekend, Obama made a surprise appearance Friday at a downtown rally promoting Chicago’s bid for the 2016 Olympics and then gave the staff at his campaign headquarters a private pep talk. A reporter outside the closed session heard him say, “If I had lost Iowa, it would have been over.”

Obama’s other remarks weren’t audible, but he was frequently interrupted by applause and cheering by staff members crowded into the room.

Clinton spent much of Friday working on her concession speech with campaign manager Maggie Williams, media adviser Mandy Grunwald and strategist Mark Penn. Aides described the process as painstaking and emotional but said there was no question Clinton would enthusiastically endorse Obama in the speech.

She also was holding a party at her Washington home Friday night to thank and bid farewell to her campaign staff.

Clinton and Obama went to great lengths to keep their meeting a secret from the media beforehand.