Edwards, who bestowed his long-sought endorsement on Obama on Wednesday, won 19 delegates before departing the presidential race in January.
Within hours, Obama picked up the backing of three of them from South Carolina, one in New Hampshire and one in Iowa.
In addition, three superdelegates - Reps. James McDermott of Washington, and Henry Waxman and Howard Berman of California - endorsed Obama.
"I believe now is the time to unite behind Barack Obama so we can be in the strongest place possible to win in November," McDermott said.
Waxman said in a statement: "I have the greatest respect and admiration for Senator Clinton and former President Clinton ... It is now clear, however, that the Democratic Party is nearing a broad consensus on our nominee."
Edwards had been backed by the United Steelworkers Union, which announced it would now support Obama. The union has 600,000 active members, many of them blue-collar workers of the type that have favored Clinton in recent primaries.
Obama also picked up the personal endorsement of superdelegate Larry Cohen, the president of the Communication Workers of America union.
Campaigning in Rapid City, S.D., Clinton spoke for the first time about Edwards' endorsement.
"I have a great deal of respect for Senator Edwards," she said in response to reporters' questions. "He and I have a lot in common ... I imagine that Senator Edwards' endorsement will be of some help to Senator Obama in Kentucky, but I think that what matters are the people who actually vote."
Clinton said she had not spoken with Edwards but had spoken with his wife, Elizabeth, about the endorsement. Clinton declined to discuss their conversation.
The delegate and labor support came despite Obama's overwhelming defeat in Tuesday's primary in West Virginia, and suggested that Clinton's argument that she would be a better general election candidate was not finding a receptive audience.
The former first lady is favored to win next week's primary in Kentucky, while Obama is expected to win in Oregon the same day.
The delegates won by Edwards are not bound by his endorsement of Obama, but several said it is important to their decision.
"I will cast my vote for who John Edwards asks me to," said Robert Groce, a South Carolina delegate won by Edwards.
Arlene Prather-O'Kane, of Cedar Falls, Iowa, said she is a backer of Edwards but "I will support who he is endorsing - which is Barack."
With the primary season winding down, both Clinton and Obama have turned their attention increasingly to the superdelegates, the members of Congress and other party officials who have seats at the convention by virtue of their positions.
Obama long trailed Clinton among superdelegates, but overtook her last week, and has pulled further away despite suffering one of his worst defeats in the campaign in West Virginia.
Clinton spent the day campaigning in South Dakota, one of two states that closes out the primary season on June 3. Obama was home in Chicago.
Both rivals had avidly sought Edwards' endorsement, particularly in the weeks after he dropped out of the race. The former North Carolina senator and 2004 vice presidential nominee had campaigned as a champion of the working class, and in the wake of his departure, Clinton consistently drew more blue-collar votes than Obama did.
"We are here tonight because the Democratic voters have made their choice, and so have I," Edwards said Wednesday to thunderous applause from an audience in Grand Rapids, Mich. He said Obama "stands with me" in a fight to cut poverty in half within 10 years, a claim Obama confirmed moments later.
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Associated Press reporters Matthew Daly and Jesse J. Holland in
Washington, Jim Davenport in Columbia, S.C., Amy Lorentzen in Des
Moines, Iowa, and Sara Kugler in Rapid City, S.D., contributed to
this report.
