Republicans objected to Perez's nomination by citing his tenure as head of the Justice Department's civil rights division. They have accused Perez of improper involvement in a whistleblower case in St. Paul, Minn.
On Wednesday, the Senate voted to move forward with a vote on Perez, with his nomination getting just enough votes — 60 — to move forward.
The Senate in recent days has also confirmed Richard Cordray as head of the Consumer Financial Protection Bureau, and Fred Hochberg as head of the U.S. Export-Import Bank.
Hilda Solis resigned as labor secretary in January.
Following the Perez vote, the Senate moved to debating Gina McCarthy's nomination as head of the Environmental Protection Agency. Her nomination is also expected to receive a vote Thursday.
Updated at 12:56 p.m.