The meeting, which lasted more than an hour, is not the only session Kerry plans with potential vice presidential candidates in the next several days, said Democratic officials who spoke on condition of anonymity because Kerry has insisted that the talks remain under wraps until he announces his nominee in July.
Kerry must make his selection before the Democratic National Convention (search), which begins July 26.
The Massachusetts senator declined to discuss his Wednesday meetings. "I'm the only one who knows what I was doing yesterday," he told American Urban Radio Networks (search) on Thursday. "I was doing work I had to do up on the Hill, and I met with a number of colleagues. But I'm not talking about" the search process.
Kerry disputed reports that his staff had settled on a schedule to announce his pick in July. "Nobody on my staff knows anything about any date," he said. "I have not made a decision about when I'm going to make an announcement."
Among the qualities he's seeking in a nominee, Kerry said, "Somebody who has the ability to fill in as president if something terrible were to happen to the president."
Al Sharpton, the political activist who challenged Kerry for the Democratic nomination, said Thursday he was offering the candidate advice on the pick but would not disclose the advice he was giving or whom he thinks Kerry should consider.
"I think it must be somebody that can energize voters and then represent where the American public is right now," Sharpton told reporters as he joined Kerry for a campaign trip to Detroit. He said he has not discussed being Kerry's running mate but plans to help the presumptive nominee court urban voters and others.
Gephardt, a former House minority leader, ran against Kerry in a crowded Democratic nominating field. A favorite of organized labor, Gephardt hails from the swing state of Missouri.
"I'm happy to do it if he wants me to do it," the lawmaker told The Associated Press before the meeting. "I'm equally happy to not do it, and just help in other ways."
The Kerry-Gephardt meeting came as another candidate, Iowa Gov. Tom Vilsack (search), made the rounds in Washington while refusing to say whether he was meeting with Kerry. However, officials close to the deliberations said he did not get together with the presumptive nominee.
Gov. Kathleen Sebelius (search) of Kansas, a Democrat touted by some party officials as a potential candidate, also was in Washington on Wednesday. She said she did not meet with Kerry.
Later, Kerry met at his Washington home with campaign manager Mary Beth Cahill and Jim Johnson, head of his vice presidential search team. Officials said Kerry did not interview candidates at his home.
He planned to meet with staff at his campaign headquarters Thursday before flying to Michigan for a fund-raiser.
Officials said Sen. Bob Graham (search) of Florida is among the Democrats expected to meet with Kerry in the coming days. They said much of Kerry's search process, including whom he is meeting with and his full list of prospects, has not been made public.
The Kerry-Gephardt meeting, conducted in Kerry's Capitol hideaway, sparked a raft of running mate rumors, a ritual in presidential politics.
"Against the backdrop of the presidential campaign, you always have this subtle, sometimes overt, unofficial campaign for vice president," said Michael Feldman, an aide to former Vice President Al Gore.
Gore watched a parade of ambitious Democrats, including Kerry, angle for a spot on the 2000 ticket. Sen. Joe Lieberman of Connecticut eventually won the veepstakes that year, edging out Kerry and a third senator, John Edwards of North Carolina, who again is running hard for the No. 2 job.
The last major candidate to bow to Kerry in the primaries, Edwards has urged his fund-raising team to help fill Kerry's coffers. The Southerner has traveled the country on behalf of the nominee-in-waiting, accusing Republicans of creating two Americas -- one for the wealthy and one for everyone else.
A recent Associated Press poll conducted by Ipsos-Public Affairs suggested that a majority of registered voters want Kerry to pick Edwards.
Four years ago, few predicted that George W. Bush would turn to Dick Cheney, who headed his search team, or that Lieberman would become the first Jewish vice presidential nominee.
"The vice presidential nomination almost always doesn't go to the person who the people most expect. That doesn't bode well for John Edwards," said Steve McMahon, adviser to former Kerry rival Howard Dean.