Republicans had demanded the records as a condition of moving forward with John Brennan's confirmation.
"The administration has agreed to provide the material, (and) some of it is going to be provided tomorrow," said Sen. Dianne Feinstein, D-Calif. "It is my hope that that is sufficient and we will be able to schedule the nomination for a vote on Thursday."
But Feinstein also said the Obama administration has not yet responded to the committee's request for more details about the classified Justice Department legal opinions that justify using unmanned spy planes to kill al-Qaida suspects overseas, including American citizens.
Feinstein said she still needs to consult with the committee's vice chairman, Sen. Saxby Chambliss, R-Ga., on the date for the vote on Brennan's nomination. She declined to specify what information on Benghazi the White House will be giving the committee.
A congressional aide said last week that the documents include emails between top national security officials showing the debate within the administration over how to describe the attack and other documents the committee had previously requested. The aide spoke on condition of anonymity because he was not authorized to discuss the matter publicly.
While the nomination appears to be headed for a committee vote, several senators said Monday they still have lingering questions and concerns about the lethal drone strikes and Brennan's knowledge about the CIA's use of harsh interrogation techniques during the Bush administration.
Brennan, 57, is a veteran of more than three decades in intelligence work. He withdrew his name from nomination to head the CIA at the start of Obama's first term amid questions about the role he played at the spy agency when the Bush administration approved waterboarding and other forms of "enhanced interrogation" of suspected terrorists.
"We need any and all legal opinions pertaining to the targeted killings, and we have not gotten that," said Sen. Ron Wyden, D-Ore., a member of the Intelligence Committee. "We need those documents in order to carry out our obligation to do vigilant oversight."
Sen. Susan Collins, R-Maine., said she is inclined to support Brennan's nomination but agreed the Justice Department opinions should be disclosed to the committee along with the Benghazi information. "It's my understanding that we're making some progress on that latter issue but not any on the former," she said.
Sen. John McCain, R-Ariz., has threatened to put a hold on Brennan's nomination unless the Benghazi information is delivered. He also has said that Brennan's positions on waterboarding and torture are inconsistent because Brennan has said he's opposed to such methods while also arguing they saved lives.
"We have a number of questions that need to be answered," McCain said.
Sen. Rand Paul, R-Ky., said last week he will filibuster Brennan's nomination unless his concerns over the legality of using drone strikes inside the U.S. are answered. Paul said he has written to Brennan three times about the extent of the government's drone authority, most recently on Feb. 21.
Brennan has told the Senate Intelligence Committee that the Obama administration has not carried out drone strikes on U.S. soil and has no intention of doing so.
But Paul said that answer is insufficient. "The question that I and many others have asked is not whether the administration has or intends to carry out drone strikes inside the United States, but whether it believes it has the authority to do so," Paul wrote. "This is an important distinction that should not be ignored."
Moira Bagley, Paul's spokeswoman, said Monday the senator has not received a response from Brennan.
Associated Press writer Donna Cassata contributed to this report.