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Republican National Committee Chairman Michael Steele said the White House response is further proof the administration needs to “open itself” to an independent investigation. 

“In the three months since Joe Sestak first made his allegation, the White House has denied, stonewalled and is now trying to downplay the claims with an unsubstantiated memo,” Mr. Steele said. “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?”

Mr. Sestak, a former Navy admiral, made the assertion about a “high-ranking” job offer at least twice — once to a local cable television interviewer Feb. 18 and again Sunday. He has steadfastly declined to say who approached him and which job was discussed. Mr. Sestak, however, has said he would cooperate in any investigation.

The White House report states rumors about Mr. Sestak being offered the job of secretary of Navy were false because Mr. Obama announced his intent to nominate Ray Mabus roughly a month before Mr. Specter switched party affiliation to Democrat.

Mr. Mabus, an ex-Navy officer and Mississippi governor, was confirmed in May. 

Among the Democrats pressing for more details are Democratic National Committee Chairman Tim Kaine; Sen. Richard J. Durbin, Illinois Democrat; and Pennsylvania Gov. Edward G. Rendell, a Democrat who supported Mr. Specter.

Before Friday, White House officials repeatedly maintained nothing inappropriate occurred, while offering few details.

As recently as Monday, senior adviser Mr. Axelrod said conversations with Mr. Sestak were “perfectly appropriate.”

He also said, however, no questions would “be left unanswered,” and that if Mr. Sestak’s assertions were true, “they would constitute a serious breach of the law.”

Among the likely other remaining questions are how the president’s in-house lawyer can be responsible for reporting legal violations, and what the scope was of the investigation — including who was interviewed.