(CNN) - Amid a press conference that largely focused on the BP oil spill in the Gulf of Mexico, President Barack Obama refuted allegations of impropriety surrounding reports that his administration offered Rep. Joe Sestak a position several months ago if he would drop his Pennsylvania Senate bid.
"I can assure the public that nothing improper took place," the President said, at the end of his hour-long press conference.
But Obama refused to give any more details on the alleged offer, even as several Republicans and a handful of Democrats have demanded the White House be more upfront on the matter.
(Updated with Sestak comments after the jump.)
"There will be an official response shortly on the Sestak issue, which I hope will answer your questions," Obama said when asked about the issue at the end of an hour press conference. "You will get it from my administration. And it will be coming out, when I say shortly, I mean shortly. I don't mean weeks or months."
Sestak defeated Sen. Arlen Specter in last Tuesday's Democratic Pennsylvania Senate primary, but three months ago - when he faced longer odds against his Democratic opponent - the Philadelphia-area congressman said that someone in the White House offered him a job on the condition that he quit the race.
Sestak has since refused to reveal any more details about the job offer – a pattern he continued earlier this week in an interview on CNN's "John King USA."
"I will let others speak for themselves," Sestak said when asked whom he talked to at the White House."I have said all I am going to say on the matter,"
White House Senior Adviser David Axelrod also told CNN earlier this week that if White House officials offered Sestak a job in exchange for abandoning the Senate race, it would constitute "a serious breach of the law."
Pressed on the matter, Axelrod would not say whether the White House planned to reveal which officials had conservations with Sestak.
On Wednesday, all seven Republican members of the Senate Judiciary Committee called for a special prosecutor to look into the matter.
UPDATE 6:50 p.m.: After Obama's press conference Thursday, Rep. Sestak told reporters that his brother Richard, who works as an attorney for Sestak's Senate campaign, was called by the White House.
Sestak said as soon as the White House releases information he will have more to say and the Pennsylvania Democrat pledged to meet with reporters to answer any further questions.
He said "I presently don't" have plans to speak with the White House before it releases its report, and he repeatedly said he did not know when the report would be issued.
Sestak maintained that the controversy over whether he was offered a job to get him not to run against Sen. Specter has not had any impact on his Senate race. "Not at all. Not at all. We have just kept on going," he said.
The Senate hopeful said that in his many campaign stops he has yet to have anyone in Pennsylvania ask him about the controversy with the exception of one reporter.
"I understand Washington, D.C. This is of interest to Washington D.C., but the fact is I was asked a question, you know, something that happened 7-8 months earlier. And if you look at the original interview I just said yes, and beyond that, anything, except this, is for others."