Sen. Dianne Feinstein, D-Calif., said she will introduce legislation next year to ban the sale of new assault weapons, as well as big clips, drums and strips of more than 10 bullets.
California's other democratic senator, Barbara Boxer, also wants to renew the assault weapons ban and limit magazine capacity to 10 rounds.
It remains to be seen whether these new developments will translate into renewed support for tighter gun control laws. A Clinton-era ban expired in 2004 and has not been renewed.
In an address to the nation, President Barack Obama didn't signal support for a specific response, but has supported gun control in the past.
"We can't tolerate this anymore. These tragedies must end and to end them we must change," the president said in a speech at a vigil held in Newtown for the victims.
More than 100 protesters took to the streets in Washington to demonstrate against the National Rifle Association, which has kept a low profile in recent days.
An exclusive Eyewitness News poll conducted by SurveyUSA shows 54 percent of people in the station's viewing area feel that to reduce gun violence it is most important to control gun ownership. Fifty-three percent say the best way to reduce gun violence is by stricter enforcement of existing laws and 58 percent support a limit on how much ammunition a gun can hold.
On the House floor, Senate Majority Leader Harry Reid (D-Nev.) read the names of the 20 children and six adults who were killed when a gunman carrying a high-powered military-style rifle and other guns stormed Sandy Hook Elementary in Newtown on Friday morning.
"Part of the healing process will require Congress to examine what can be done to prevent more tragedies," Reid said.
New York Mayor Michael Bloomberg wants a ban on assault weapons nationwide.
"This is just ridiculous," he said. "This is an outrage. We are killing each other and we are the only industrialized country in the world doing it."
"Everything should be on the table," West Virginia Sen. Joe Manchin declared Monday. He is a conservative Democrat, avid hunter and lifelong member of the National Rifle Association. Republican Sen. Chuck Grassley of Iowa proposed a debate not just about guns but also about mental issues.
Other members of Congress said they believe school staff should be allowed to have firearms to protect children.
"She takes him out, takes his head off, before he can kill those precious kids," said Rep. Louis Gohmert, R-Texas, during an appearance on Fox News.
The Associated Press contributed to this report.
