WASHINGTON -LRB- CNN -RRB- -- 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 did n't shed any light on whether Clinton would have a place on the ticket . `` Hillary is going to endorse Barack -LSB- on Saturday -RSB- , '' 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 -LSB- election -RSB- , 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 was n'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. -LSB- John -RSB- McCain and the Republicans . '' Read Clinton 's message to supporters -LRB- PDF -RRB- 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 did not concede defeat that night . Instead , she asked supporters to visit her Web site and give her advice on how to proceed . Obama has named Caroline Kennedy , daughter of President Kennedy , and former Deputy U.S. Attorney General Eric Holder to a vice presidential selection team led by former Fannie Mae CEO Jim Johnson . CNN 's Ted Barrett and Candy Crowley contributed to this report .