The Republican-controlled committee advanced an Outer Continental Shelf transboundary agreement on a 25-16 vote, largely along party lines.
The measure, if passed, would give energy companies access to as much as 172 million barrels of oil and 304 billion cubic feet of natural gas.
"This is a common sense approach to work with our partners south of the border to make both countries more energy secure, while protecting our sovereignty," U.S. Rep. Jeff Duncan, S.C., who introduced the bill, said in a statement.
Sierra Club representative Athan Manuel told the committee last month that more drilling in the Gulf of Mexico isn't needed because energy companies have enough work on their hands.
U.S. Rep. Ed Markey, D-Mass, ranking member on the committee, published a report last week that said safety concerns were a factor to consider more than two years after the BP spill in the Gulf of Mexico.
Republican leaders in the House of Representatives have, in general, pressed for fewer restrictions on domestic oil and natural gas exploration.
A U.S.-Mexico agreement signed last year called for a joint inspection team to ensure compliance with applicable safety and environmental laws in the maritime area.