The action by the House Rules Committee sets the stage for preliminary and final votes on Wednesday.
The House is expected to reconvene around 5 p.m. Tuesday night and the delay any action on the bill until 10 a.m. Wednesday in order to give Republican lawmakers an opportunity to prepare amendments to the bill.
House Speaker Michael Busch said debate on the bill and the amendments could be extended.
"It's going to be a long day," Busch said, adding that he hoped to complete work on the bill by early afternoon.
The action by the House of Delegates comes after the Senate voted 33-13 to approve O'Malley's proposed redistricting plan.