The vote Wednesday was 10-7, with one senator voting present. The full Senate is expected to vote on the measure next week.
The resolution would permit Obama to order a limited military mission against Syria, as long as it doesn't exceed 90 days and involves no American troops on the ground for combat operations.
The Democratic chairman of the Foreign Relations Committee, Sen. Bob Menendez, and the panel's top Republican, Sen. Bob Corker, crafted the resolution.
The vote marked the first time lawmakers have voted to authorize military action since the October 2002 votes giving President George W. Bush the authority to invade Iraq.
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