WASHINGTON — For three months, the White House has refused to say whether it offered a job to Representative Joe Sestak to get him to drop his challenge to Senator Arlen Specter in a Pennsylvania Democratic primary, as Mr. Sestak has asserted.

But the White House wants everyone who suspects that something untoward, or even illegal, might have happened to rest easy: though it still will not reveal what happened, the White House is reassuring skeptics that it has examined its own actions and decided it did nothing wrong. Whatever it was that it did.

“Lawyers in the White House and others have looked into conversations that were had with Congressman Sestak,” Robert Gibbs, the White House press secretary, said Sunday on “Face the Nation” on CBS. “And nothing inappropriate happened.”

“Improper or not, did you offer him a job in the administration?” asked the host, Bob Schieffer.

“I’m not going to get further into what the conversations were,” Mr. Gibbs replied. “People that have looked into them assure me that they weren’t inappropriate in any way.”