NEW YORK — Angling for a vice presidential nod, Hillary Rodham Clinton refused to bow out of the Democratic race Tuesday, hoping to maintain leverage as Barack Obama clinched the delegates needed to secure the party's nomination.

"A lot of people are asking, 'What does Hillary want,' " Clinton told supporters at a rally in New York City. "I want what I have always fought for: I want the nearly 18 million people who voted for me to be respected and heard."

Clinton told the crowd she would consult in the coming days with advisers about the fate of her moribund candidacy. But her remarks came hours after she told congressional colleagues she would be open to joining Obama as his running mate.

Many of her top supporters spoke openly of Clinton's potential vice presidential prospects. Lanny Davis, a former White House special counsel under President Clinton, said he told the former first lady

Tuesday that he was initiating a petition to press Obama to select her for the second spot on the ticket. He said Clinton did not encourage or discourage the step.

"If he doesn't have her, I think he can still win. With her on the ticket, he can't be beat," Davis said.

Clinton's national finance chairman, Hassan Nemazee, said he was also pushing an Obama-Clinton ticket, claiming that together they would be able to raise $200 million to $250 million for the general election.

Advisers indicated earlier Tuesday that the former first lady would publicly acknowledge in her speech that Obama had crossed the delegate threshold. But she refused to do so even after television networks and The Associated Press declared the Illinois senator had sealed the nomination.

Her advisers said they considered the delegate numbers to be unreliable, even as The Associated Press estimated he had several more than the 2,118 needed to nominate. Earlier, Clinton acknowledged on a conference call with New York lawmakers that the delegate math was not there for her to overtake Obama, according to several participants on the call.

She said none of that publicly Tuesday but vowed the Democratic Party would unite in its effort to defeat Republican John McCain in November.

Clinton won South Dakota's primary Tuesday, while Obama won Montana's. The two contests rounded out an historic 5-month primary battle that pitted the first major black candidate against the first serious woman contender.

On the conference call with New York colleagues, Clinton, a New York senator, said she would be willing to become Obama's running mate if it would help Democrats win the White House.

Clinton's remarks came in response to a question from Democratic Rep. Nydia Velazquez, who said she believed the best way for Obama to win key voting blocs, including Hispanics, would be for him to choose Clinton as his running mate.

"I am open to it," Clinton replied, if it would help the party's prospects in November. Her direct quote was described by two lawmakers who spoke on condition of anonymity because they were not authorized to speak for Clinton.

"I deserve some time to get this right," she said, even as the other lawmakers forcefully argued for her to press Obama to choose her as his running mate.

Joseph Crowley, a Queens Democrat who participated in the call, said her answer "left open the possibility that she would do anything that she can to contribute toward a Democratic victory in November. There was no hedging on that. Whatever she can do to contribute, she was willing to do."

Another person on the call, Rep. Jose Serrano of New York City, said her answer was "just what I was hoping to hear."

Rep. Charles Rangel, a devoted booster of Clinton who helped pave the way for her successful Senate campaign, said he spoke to her Tuesday and got much the same answer.