The report didn't impress Republicans.
"This memo frankly raises more questions: What was Bill Clinton authorized to offer? Did President Obama sign off on this conversation before it took place?" Republican National Committee Chairman Michael Steele said.
"Now more than ever it is clear that this White House is not capable of policing itself and needs to open itself to an independent investigation."
Rep. Darrell Issa, the top Republican on the House oversight committee who unsuccessfully had sought a Department of Justice investigation, said Obama had become a part of the Washington culture he decried.
"Regardless of what President Clinton or Congressman Sestak now say, it is abundantly clear that this kind of conduct is contrary to President Obama's pledge to change 'business as usual' and that his administration has engaged in the kind of political shenanigans he once campaigned to end," Issa said.
Sestak, who had said a job was offered but had provided no details, acknowledged Friday that he had had the conversation with Clinton. He said the former president told him he should stay in the U.S. House and perhaps join a presidential board.
In a statement released by his campaign, Sestak said, "I said no. I told President Clinton that my only consideration in getting into the Senate race or not was whether it was the right thing to do for Pennsylvania working families and not any offer."
Specter declined to comment.
The report said White House Chief of Staff Rahm Emanuel enlisted Clinton's help as a go-between with Sestak. Clinton agreed to raise the offer of a seat on a presidential advisory board or another executive board if Sestak dropped his bid, "which would avoid a divisive Senate primary," the report said.
Under the proposed arrangement, Sestak would have been able to remain in the House while serving on a board. It was not clear why the White House -- which has the power to offer Cabinet posts and sought-after embassy jobs -- believed Sestak would be interested in just an advisory position.
Sestak defeated the five-term Specter, who had switched from Republican to Democrat last year at the White House's urging, in the May 18 Democratic primary.
Emanuel and Sestak both worked in the White House when Clinton was president in the 1990s, and both remain close with their former boss. Sestak was a supporter of Clinton's wife, Hillary Rodham Clinton, in her 2008 presidential bid.
Bauer, in the White House report, argued that previous Democratic and Republican administrations, "motivated by the same goals, discussed alternative paths to service for qualified individuals also considering campaigns for public office." The report said such actions aren't illegal nor unethical.
For weeks, the White House had insisted officials did not behave inappropriately but had declined to elaborate. But after Sestak won the nomination, Republicans renewed their questions of the administration and White House lawyers prepared to release a report they had been compiling for months.
At a White House news conference on Thursday, Obama told reporters a full accounting would be forthcoming.
"I can assure the public that nothing improper took place," he said.
Two top Democrats -- party chief Tim Kaine and Dick Durbin of Illinois, the party's second-ranking leader in the Senate -- said during the week that the White House and Sestak needed to address the questions. So, too, did Sestak's Republican challenger in Pennsylvania, former Rep. Pat Toomey.