WASHINGTON (CNN) -- Barack Obama and Hillary Clinton met privately Thursday night at the Washington home of Sen. Dianne Feinstein, a key supporter of Clinton's presidential campaign, Feinstein said Friday.



Sens. Hillary Clinton and Barack Obama speak Wednesday at the AIPAC meeting.



She left them in her living room with nothing other than water and comfortable chairs for what she called a positive meeting. No one else was in the room, and no one is giving details of what was discussed.



"They talked. I went upstairs and did my work," Feinstein said Friday. "They called me when it was over. I came down and said, 'Good night, everybody; I hope you had a good meeting.'



"They were laughing, and that was it."



The meeting began at 9 p.m. and lasted about an hour, Feinstein said.



"I think the opportunity to sit down, just the two of them, was positive," she said.



It was the two Democratic candidates' first meeting since Obama became the party's presumptive nominee Tuesday.



"They talked about how to come together and how to unify this party and move forward because what we have at stake in November is so important," Robert Gibbs, the Obama campaign's communication director, said Friday on CNN's "American Morning."  Watch Gibbs explain the secret meeting »



"And what unites us as a party far exceeds what might divide either of these two candidates."



A joint statement from the candidates said only, "Sen. Clinton and Sen. Obama met tonight and had a productive discussion about the important work that needs to be done to succeed in November."



Gibbs would not say whether the senators discussed the possibility of Clinton becoming Obama's running mate.Senate Majority Leader Harry Reid, a Democratic superdelegate from Nevada, said Friday that he told Clinton he intended to support Obama. But he didn't shed any light on whether Clinton would have a place on the ticket.



"Hillary is going to endorse Barack [on Saturday]," Reid said on "American Morning." "She's a very good woman. She's been a great senator. And she's going to be a great help to us in this [election], no matter what role she has in the campaign."



On Thursday, reporters on Obama's press plane learned that the candidate was not aboard when it departed Virginia, where he had been campaigning. Aides said staff members had "scheduled him some meetings" in Washington.



The meeting originally was believed to be at Clinton's Washington home.



"It wasn't at her house, and it was not at Dick Cheney's undisclosed location," Gibbs said jokingly.



Also Thursday, Clinton thanked supporters in an e-mail and pledged to help Obama capture the White House after eight years of Republican control. Clinton also plans to thank supporters Saturday at a Washington event.



"I have said throughout the campaign that I would strongly support Sen. Obama if he were the Democratic Party's nominee, and I intend to deliver on that promise," the e-mail read.



"This has been a long and hard-fought campaign, but as I have always said, my differences with Sen. Obama are small compared to the differences we have with Sen. [John] McCain and the Republicans." Read Clinton's message to supporters (PDF)



Clinton plans to suspend her campaign within days, her campaign said. By suspending instead of dropping out, Clinton technically would remain a candidate, entitled to keep statewide pledged delegates and district-level delegates.



Democrats nationwide have coalesced around Obama since he received enough delegates to win the nomination Tuesday evening.



The New York Democratic congressional delegation embraced Obama's candidacy Thursday on the steps of the U.S. Capitol. iReport.com: Should Obama pick Clinton?



On Friday, Democratic leaders in New York, including state legislators and City Council members, endorsed Obama at New York's City Hall, sources said.



Obama earned enough delegates Tuesday to clinch the nomination, but Clinton
Who will Sen. Hillary Clinton endorse?
Barack
question: Who will Sen. Hillary Clinton endorse?, answer: Barack