"It is the chairman's intention to vote on the nomination after the members have an opportunity for discussion," committee Chairman Levin, D-Mich., said in a statement.
"I don't think we should allow Brennan to go forward for the CIA directorship, Hagel to be confirmed to secretary of Defense until the White House gives us an accounting (on Libya)," said Graham.
Former U.S. Secretary of State Hillary Clinton was questioned about the State Department's response to a 2012 attack in Libya that left U.S. Ambassador to Libya Chris Stevens and three of his staff members dead.
Hagel faced frustrated Republican senators during his nomination hearing earlier this month. His stance on Iran and Iraq was seen as out of step with his former colleagues' positions.
Last week, Levin expressed concern that Republicans were over-reaching with their objections to Obama's nominees.