WASHINGTON — Likely Democratic nominee Senator Obama has begun a top-secret search for a running mate, fresh signs that the general election campaign is well under way and the primary race against Senator Clinton is basically over.

Mr. Obama has asked a former Fannie Mae CEO, Jim Johnson, to begin vetting potential vice presidential picks, Democratic officials said today. Mr. Johnson did the same job for Democratic nominees Senator Kerry in 2004 and Vice President Mondale in 1984.

Mr. Obama refused to acknowledge Mr. Johnson’s role when The Associated Press asked the Illinois senator about it in the Capitol today.

“I haven’t hired him. He’s not on retainer. I’m not paying him any money. He is a friend of mine. I know him,” Mr. Obama said. “I am not commenting on vice presidential matters because I have not won this nomination.”

The Democratic officials spoke on a condition of anonymity about a process that the campaign wants to keep quiet.

Vice presidential searches are usually closely held secrets, but Obama campaign officials say the effort is being handled by a particularly tight circle of advisers.

The campaign did not want to discuss the effort because they are still engaged in a fading primary campaign against Mrs. Clinton, with three primaries left in Puerto Rico, South Dakota, and Montana. The voting ends June 3. Mr. Obama has repeatedly declined to discuss possible running mates while the primary is ongoing.

“We’re not commenting about this process,” an Obama spokesman, Bill Burton, said.

But they are taking behind-the-scenes steps to move toward the general election campaign, with just 61 delegates needed to clinch the nomination according to the latest Associated Press count. Mr. Obama has 1,965 delegates to Mrs. Clinton’s 1,780, with 2,026 required to secure the party’s nod under Democratic National Committee rules.

The Obama campaign is rapidly adding to its campaign staff, both at the headquarters and in general election swing states. Mr. Obama has been traveling to some of those battlegrounds — Missouri, Michigan, Iowa, and Florida in the last nine days — while the campaign is registering voters across the country for the November vote. And a top Obama organizer, Paul Tewes, is in discussions to take over the Democratic National Committee.

It’s all part of an effort to lay the groundwork for an aggressive kickoff to a general election campaign. Senator McCain has a head start and has been building his effort for several months since the Republican primary race wrapped up in early March.

Mr. McCain is hosting at least three Republicans mentioned as potential vice presidential running mates at his Sedona, Ariz., home this weekend — Governor Crist of Florida, Governor Jindal of Louisiana, and the former Massachusetts Governor, Mitt Romney. A top aide said it’s a social event with more than two dozen guests not meant for veep vetting.

Mr. Obama’s campaign refused to talk about who was being considered, but some in the party are calling for him to pick Mrs. Clinton. A Clinton spokesman, Howard Wolfson, said today, “There have been no discussions with the Obama campaign about Senator Clinton being the V.P.”

Other possible options are governors such as Janet Napolitano of Arizona, Kathleen Sebelius of Kansas, and Tim Kaine of Virginia; foreign policy experts like the former Georgia senator, Sam Nunn, Senator Dodd of Connecticut, or Senator Biden of Delaware; or other senators such as Claire McCaskill of Missouri and Jim Webb of Virginia.

He could look outside the party to people such as the war critic Senator Hagel, a Republican of Nebraska, or Mayor Bloomberg. Or he could look to one of his early prominent supporters such as the former senator of South Dakota, Tom Daschle, or the 2004 vice presidential nominee, John Edwards. Or he could try to bring on a Clinton supporter like Senator Bayh of Indiana.

Johnson’s role running the veep process was first reported on TheAtlantic.com.