Washington (CNN) -- White House Chief of Staff Rahm Emanuel used former President Bill Clinton as an intermediary last year as part of a failed administration effort to dissuade Pennsylvania Rep. Joe Sestak from running for the U.S. Senate, according to a publicly released memorandum from the White House legal counsel's office.

Top White House lawyer Robert Bauer conceded that "options for Executive Branch service were raised" for Sestak, but insisted that administration officials did not act improperly. He characterized the attempt to influence Pennsylvania's Democratic Senate primary -- ultimately won by Sestak -- as no different from political maneuvers by past administrations from both political parties.

Key Republicans disagreed with Bauer's assessment. Several House GOP members sent a letter to the FBI Friday asking for an investigation.

The White House was instrumental in last year's switch by Pennsylvania Sen. Arlen Specter from the GOP to the Democratic Party. President Barack Obama backed Specter in his bid for a sixth term in the Senate, and the administration was eager to clear the field of any primary opponents.

Bauer stated in the memo that efforts "were made in June and July of 2009 to determine whether Congressman Sestak would be interested in service on a presidential or other Senior Executive Branch Advisory Board, which would avoid a divisive Senate primary, allow him to retain his seat in the House, and provide him with an opportunity for additional service to the public in a high-level advisory capacity."

Sestak would not have been paid for any advisory work, Bauer insisted.

Emanuel "enlisted the support of former President Clinton who agreed to raise with ... Sestak options of service," Bauer said. Sestak declined the suggested options, he said.

"Last summer, I received a phone call from President Clinton," Sestak confirmed Friday in a written statement. "During the course of the conversation, he expressed concern over my prospects if I were to enter the Democratic primary for U.S. Senate. ... He said that White House Chief of Staff Rahm Emanuel had spoken with him about my being on a presidential board while remaining in the House of Representatives. I said no."

Bauer said that the White House, contrary to one widely circulated rumor, did not offer Sestak the position of secretary of the Navy. He noted Obama nominated Ray Mabus for the position on March 26, 2009, more than a month before Specter switched to the Democratic Party.

Bauer insisted there was no impropriety in the White House's efforts.

"The Democratic Party leadership had a legitimate interest in averting a divisive primary fight and a similarly legitimate concern about the congressman vacating his seat in the House," he wrote. The White House's attempt to keep Sestak out of the Senate race was "fully consistent with the relevant law and ethical requirements."

California GOP Rep. Darrell Issa, who has pushed for the appointment of a special prosecutor to examine the incident, vehemently disagreed with Bauer's conclusions.

The White House "has admitted to a misdemeanor ... and co-opted President Clinton" in it, Issa insisted. "Is Rahm Emanuel going to stay if in fact he violated the law?"

Clinton "of all people would be held to a standard of knowing exactly where the line is," Issa said. "If he crossed it, he crossed it knowingly."

Issa said that it is "not the job offer [but] the quid pro quo. ... It's the 'I will give you this job to clear a primary.' "

Issa joined several other House Republicans in urging the FBI to investigate allegations of bribery.

"Assurances by the Obama White House that no laws were broken are like the Nixon White House promising it did nothing illegal in connection with Watergate. Clearly, an independent investigation is necessary to determine once and for all what really happened," they wrote in a letter to FBI Director Robert Mueller.

Sestak, a former Navy admiral and two-term Philadelphia-area congressman, dismissed the GOP's allegations of wrongdoing, telling reporters that if he had thought something was wrong, he would have reported it.

"Washington, D.C., is often about political deals," Sestak said. He insisted that Clinton spoke to him only once about the proposal.

Obama said Thursday that he can "assure the public that nothing improper took place." The president, however, refused to give any more details, even as some Democrats have demanded the White House be more forthcoming about the matter.

Since Sestak's May 18 primary victory, Republicans have been relentless in keeping the controversy in the news. On Wednesday, all seven Republican members of the Senate Judiciary Committee called for a special prosecutor to look into the matter.

One of the unpaid positions that the White House suggested offering Sestak was an appointment to the president's Intelligence Advisory Board, which gives the president independent oversight and advice. But it was determined that Sestak could not serve on the board, since he was an active a member of Congress.

It appears that Emanuel picked Clinton as a go-between with Sestak because of the former president's stature as an elder statesman and prominent figure in the Democratic Party, and because Sestak worked on the National Security Council during Clinton's years in the White House. Sestak backed former first lady and then-Sen. Hillary Clinton in the 2008 Democratic presidential primaries.

According to a source at the State Department, Emanuel remains on a trip to Israel and is not expected to be back in the country until Monday.

CNN's Dana Bash, John King, Suzanne Malveaux and Deirdre Walsh contributed to this report.