The former Arizona congresswoman was a victim of a 2011 Tucson shooting that left six people dead.
"I know they got into politics for the same reason I did - to make a difference, to get things done", Giffords' statement said.
But so far there is no indication that Republicans will take up gun violence legislation.
Trump's predecessor Barack Obama frequently used mass shootings to call for stricter gun control laws.
Lt. Governor Ralph Northam, who has made stricter gun laws a central plank in his campaign for the commonwealth's top office, canceled a series of events with Giffords and Kelly created to highlight his differences with the Republican nominee, former George W. Bush adviser Ed Gillespie, on the issue of "the epidemic of gun violence". "Do not wait. The nation is counting on you".
Opponents of the measure say that the silencer provision, in particular, could make it harder to identify a shooter during an incident such as the one in Las Vegas.
Senate Minority Leader Chuck Schumer, D-N.Y., added his name to a growing list of Democratic lawmakers calling on Congress to pass stronger gun control laws.
Google admits citing 4chan to spread fake Vegas shooter news
The Gateway Pundit article made it on Facebook's crisis response page about the shooting, which Facebook now "deeply regrets". Facebook also creates a dedicated page where users can check in on friends in the affected area and see breaking news.
"We can't just be working to defeat bad legislation like federally mandated concealed-carry and the deregulation of silencers", Kelly said. "There's a lot we need to do in the wake of this mass shooting".
Republicans who reacted to the violence in Las Vegas early Monday did not call for any legislative response to the shooting. Americans need more than our president's prayers. "None of this ends unless we do something to stop it".
"I am following the details of the horrific shooting that happened in Las Vegas", Rep. Trent Franks, R-Glendale, said in a tweet Monday.
Scalise, a Louisiana Republican, returned to the Capitol last week after he was shot and critically wounded in June as he and fellow Republicans practiced for a congressional baseball game.
Videos of the initial gunfire in Las Vegas appeared to indicate the use of a fully automatic, machine-gun-type weapon.
Giffords and her husband were planning to praise Northam for supporting "responsible gun violence prevention policies" at a series of roundtable discussions in northern Virginia.
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