"It can be done," Feinstein told NBC's "Meet the Press" of reinstating the ban despite deep opposition by the powerful National Rifle Association and similar groups.
Bloomberg said Obama could use executive powers to enforce existing gun laws, as well as throw his weight behind legislation like Feinstein's.
"It's time for the president, I think, to stand up and lead and tell this country what we should do — not go to Congress and say, 'What do you guys want to do?'" Bloomberg said."
Gun-rights activists had remained largely quiet on the issue since Friday's shooting, all but one declining to appear on the Sunday talk shows.
David Gregory, the host of "Meet the Press," said NBC invited all 31 "pro-gun" senators to appear on Sunday's show, and all 31 declined. All eight Republicans on the Senate Judiciary Committee were unavailable or unwilling to appear on CBS' "Face the Nation," host Bob Schieffer said.
Rep. Louie Gohmert, R-Texas, was the sole representative of gun rights' activists on the various Sunday talk shows. In an interview on "Fox News Sunday," Gohmert defended the sale of assault weapons and said that the principal at Sandy Hook Elementary School, who authorities say died trying to overtake the shooter, should herself have been armed.
"I wish to God she had had an M-4 in her office, locked up so when she heard gunfire, she pulls it out and she didn't have to lunge heroically with nothing in her hands. But she takes him (the shooter) out, takes his head off before he can kill those precious kids," Gohmert said.
Gohmert also argued that violence is lower in cities with lax gun laws, and higher in cities with stricter laws.
"The facts are that every time guns have been allowed — conceal-carry (gun laws) have been allowed — the crime rate has gone down," Gohmert said.
Gun-control advocates say that isn't true. A study by the California-based Law Center to Prevent Gun Violence determined that 7 of the 10 states with the strongest gun laws — including Connecticut, Massachusetts and California — are also among the 10 states with the lowest gun death rates.
"If you look at the states with the strongest gun laws in the country, they have some of the lowest gun death rates, and some of the states with the weakest gun laws have some of the highest gun death rates," said Brian Malte of the Brady Campaign to Prevent Gun Violence.
Associated Press writers Jim Kuhnhenn and Josh Lederman contributed to this report.