Levin is chairman of the Senate Armed Services Committee, which needs to vote on Hagel's nomination to replace Defense Secretary Leon Panetta before the process can proceed to the full Senate. Levin said no such vote has been scheduled.
"I had hoped to hold a vote on the nomination this week but the committee's review of the nomination is not yet complete. I intend to schedule a vote on the nomination as soon as possible," Levin said in a statement.
Hagel, R-Neb., faced criticism from fellow Republicans during a nomination hearing last week. Sen. John McCain, R-Ariz., questioned Hagel's positions on war strategy in Iraq under former President George W. Bush.
Hagel, a decorated Vietnam War veteran, has received backing from Panetta and U.S. Army Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff.
Sen. Lindsey Graham, R-S.C., member of the Senate Armed Services Committee, this week expressed concern that Hagel was out of step with the U.S. position on Iran and urged President Barack Obama to reconsider the nomination.
"Chuck Hagel is a good man but these are dangerous times," Graham said in a statement.
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