Nov. 14, 2012 -- In light of calls from several senators and congressional representatives, Gen. David Petraeus has agreed to testify before the Senate Thursday, despite an FBI investigation that led to former Afghanistan general's resignation from his post as CIA-director.

The strange scandal that implicated top U.S. general and a Florida socialite and put a hold on the Senate confirmation of Gen. John Allen was thought to have robbed intelligence committees of Petraeus' testimony about the attack on the U.S. consulate in Benghazi. That attack claimed the lives of four Americans, including U.S. Ambassador to Libya Chris Stevens. Petraeus had personally flown to Libya on a fact-finding mission in late October.

The sex scandal has also raised questions about the separation of powers, and has caused some lawmakers to bristle that they were not told of the FBI's investigation sooner.

Brian Darling, senior government fellow at the Heritage Foundation, said some members of Congress were relying on the media for information that they should have been briefed on.

But Chair of the Senate Intelligence Committee Dianne Feinstein, D-Calif., told ABC News Wednesday that Petraeus was willing to come before the committee and details were being worked out.

Republican senators and representatives – and at least one top Democrat – urged the former Afghanistan general to testify, despite his resignation from his post as CIA director.

Sen. Susan Collins, R-Maine, said it was "absolutely imperative" for the Senate to hear from Petraeus.

"There are so many unanswered questions at this point," Collins said outside her office Tuesday morning. "I will say that it is absolutely imperative that Gen. Petraeus come and testify. He was CIA director at the time of the attack. He visited Libya after the attack. He has a great deal of information that we need in order to understand what went wrong."

Petraeus was scheduled to testify at a Senate Intelligence hearing on Benghazi, set for 2:30 p.m. Thursday, but because of his resignation in light of the disclosure of his affair with biographer Paula Broadwell, Acting CIA Director Mike Morell was scheduled to appear in his place at the closed-door hearing.

Senate Intelligence Committee members are likely to meet casually today to discuss what to do next regarding Petraeus, according to an aide to Feinstein, but so far no additional meetings or hearings have been scheduled in regards to Petraeus' extramarital affair, nor Benghazi.

"I think we should go ahead with Mike Morell and the way it is now set up," Feinstein said on MSNBC Monday. "But I also think that the community should know that this is not sufficient. And I have no doubt now that we will need to talk with David Petraeus, and we will likely do that in closed session, but it will be done one way or the other."

On the day Petraeus announced his resignation, Rep. Peter King, R-Iowa, said on CNN there were answers to questions on the Benghazi attack "that only he has."

"He's an absolutely necessary witness," King said.

Sen. Lindsey Graham, R-S.C., said "it is absolutely essential" for Petraeus to speak to the Senate Intelligence Committee.

"I don't see how in the world you can find out what happened in Benghazi before, during and after the attack if Gen. Petraeus doesn't testify," Graham said on CBS' "Face the Nation" Sunday.

Tea Party Republican Rep. Jason Chaffetz of Utah said Tuesday on CNN that it was possible that members of Congress could compel Petraeus to testify and Darling of the Heritage Foundation confirmed that.

"There is precedent for Congress to issue subpoenas for former administration officials," Darling said.

In the 2007 case of former White House counsel Harriet Miers, and in 1989, of former HUD Secretary Samuel Pierce, Congress issued subpoenas for their testimony.

"We could, but I don't want to take our eye off the ball," Chaffetz said. "We have four dead Americans. We've got people in the hospital tonight. We've got embassies all over the world that need time and attention. And I don't want to let, you know, a salacious story distract from the fact that Gen. Petraeus should put his duty, his honor, his country first and foremost and testify before Congress."

White House Press Secretary Jay Carney Tuesday said the president had no say in whether Petraeus will speak about the Sept. 11 attack in Libya.

"It is up to Congress to make decisions about who is called to testify," Carney said, "but the president is confident that Acting Director Morell is fully informed and capable of representing the CIA in a hearing about the incident in Benghazi."

House Minority Leader Nancy Pelosi told reporters it remained to be seen whether Congress should have been informed about the FBI investigation into Petraeus' extramarital affair earlier, but said she expected it was not of high enough importance to require they be briefed.

"I think there's some answers that we have to have about notification to Congress. I don't have any reason to think that there are any national security issues at stake in what has transpired," Pelosi said at a ceremony welcoming new Democrats to Congress. "I think some dishonorable things were done, and the honorable thing has to be to resign or not to go forward."

But Darling said Pelosi was wrong in saying Petraeus' personal indiscretion did not affect national security.

"Clearly, Congress should have been informed, and there's evidence that some members of Congress were informed before the elections," Darling said. "A scandal like that, which could impact the way that a CIA director operates, should be shared with Congress."

ABC News' Sunlen Miller and Z. Byron Wolf contributed to this report.