WASHINGTON — Forced to disclose backstage political bargaining, President Obama’s embarrassed White House said Friday it had enlisted Bill Clinton to try to ease Rep. Joe Sestak out of Pennsylvania’s Senate primary with a job offer.

Nothing wrong with that, the White House said. Oh, yes, there was, Republicans countered.

The administration admission — it said Chief of Staff Rahm Emanuel had asked the former president to call Sestak — left many questions unanswered, and it seemed unlikely the issue had been put to rest.

For Obama, the revelations called into question his promises to run an open government that was above back-room deals.

And for Sestak, they raised questions why he kept talking about the offer — a 60-second conversation, he said Friday — in the first place. “I wasn’t interested, and that was the bottom line,” Sestak said on the steps of the Capitol.

Seeking to quiet the clamor over a possible political trade, the White House released a report describing the offer that was intended to clear a path for Sen. Arlen Specter to win the Democratic nomination.

Sestak stayed in the race and eventually defeated Specter to become the Democratic nominee, ending Specter’s 30-year Senate tenure.

After a week of silence, Sestak answered reporters’ questions on last summer’s offer.

He said he cut Clinton short after hearing only a few words about a possible post on a presidential board and said the former president immediately dropped the subject.

“There was nothing wrong that was done,” Sestak said.

White House Counsel Robert Bauer rendered his own verdict in a two-page report that said there was no improper conduct in the offer. No one in the administration discussed the offer with Sestak, Bauer said.

The report did not say what, if any, contacts or promises the White House had with Specter on the matter. It also did not reveal whether Obama was aware of Clinton’s role.

White House lawyers prepared the summary weeks ago, and earlier this week, they shared it with representatives for Sestak and for Clinton. Bauer based his determination on conversations with White House officials and did not speak directly with Sestak or Clinton before reaching a conclusion.

Clinton and Obama shared a private lunch at the White House on Thursday, although White House press secretary Robert Gibbs said he was not aware whether the Pennsylvania primary was a topic.

Rep. Darrell Issa, the top Republican on the House oversight committee who unsuccessfully had sought a Justice Department investigation, said Obama had become a part of the Washington culture he decried.

“It’s pretty clear from the White House statement that they intended to get him out of the race by offering him a position, and that’s illegal and it’s unethical,” Issa said just moments after Sestak spoke.

Said Republican National Committee Chairman Michael Steele: “The memo frankly raises more questions: What was Bill Clinton authorized to offer? Did President Obama sign off on this conversation before it took place?”Sestak, who had said a job was offered but had provided no details, acknowledged Friday that he had had the conversation with Clinton.

Specter declined to comment, as did Clinton.