WASHINGTON — The Senate Judiciary Committee approved a bill Thursday to combat gun trafficking, the first firearms measure since the Newtown, Conn., shooting to move to consideration by the full Senate.

The proposal, steered by committee chairman Sen. Patrick Leahy, D-Vt., defines and imposes strict penalties for so-called straw purchasing, the act of buying a firearm for someone who cannot legally buy one themselves. The bill would also toughen punishment for selling weapons to a prohibited person.

“Law enforcement officials have consistently called for a firearms-trafficking statute that can be effective to go after straw purchasers,” Leahy said at the opening of the committee’s meeting. “What we need to do now is to create better law enforcement tools.”

The measure passed by an 11-7 vote; all 10 Democrats on the committee approved the bill, along with Sen. Charles E. Grassley of Iowa, the top Republican on the panel.

Grassley’s support came after weeks-long negotiations with Democrats. Earlier this week, Leahy introduced a modified version of the bill that blended his original proposal, written with Sen. Richard J. Durbin, D-Ill., with a measure written by Sens. Kirsten Gillibrand, D-N.Y., and Mark Steven Kirk, R-Ill. Republican Sen. Susan Collins of Maine also signed on to the measure, lending the bill the most GOP support of the gun control proposals currently being considered by Congress.

Those changes, plus the incorporation of a Grassley-sponsored amendment that would ban the Department of Justice from conducting “gun walking” operations, such as the controversial “Fast and Furious” program, without direct supervision by top Justice officials, secured Grassley’s vote.

But other Republicans on the committee withheld their support, stating that what was needed was not additional laws but better enforcement of already-existing statutes.