Reps. Jason Chaffetz, R-Utah, and Heath Shuler, D-N.C., who both hold conceal and carry permits, told Politico they would not carry the weapons in the District of Columbia.
Members of Congress get some protection from the U.S. Capitol Police, but many travel only with unarmed staffers and are not guarded when away from the Capitol.
Capitol Police held a conference call with more than 800 lawmakers, family and staff Sunday, and Speaker John Boehner, R-Ohio, told members the House sergeant-at-arms, Capitol Police and the FBI will brief them Wednesday, CBS News reports.
"We're all in this together," said Democratic Caucus Chairman John Larson, D-Conn.
Giffords, D-Ariz., was critically wounded in the head, six others were killed and others wounded during a supermarket parking lot meet-and-greet event in Tucson, Ariz., Saturday. A 22-year-old suspect is in custody.