Appearing on CNN's "State of the Union," Feinstein said restricting access to such high-powered firearms was becoming increasingly important and was gaining support from law enforcement and municipal leaders.
"Do military style assault weapons belong on the streets of our cities? And the answer, according to the United States Conference of Mayors, according to major chiefs of police, according to the largest police organization in the world, is absolutely no," Feinstein said. "So we do have support, don't mistake it."
Feinstein -- who introduced a bill Thursday to ban more than 150 types of semi-automatic weapons with military-style features -- said Sunday the most recent mass shooting in the United States were carried out by "younger and younger people" armed with such weaponry.
Feinstein, a top Democrat on the Senate Judiciary Committee, told CNN if restrictions on assault weapons were taken out of legislation on ammunition or high-capacity magazines, she would be willing to re-introduce it as an amendment on the Senate floor.
"I have been assured by the majority leader that I will be able to do it as an amendment on the floor," Feinstein said. "So that doesn't particularly bother me."
In addition to banning the manufacture, sale, transfer or importation of semi-automatic rifles and pistols that can accept detachable magazines and have at least one military feature, the legislation -- titled "The Assault Weapons Ban of 2013" -- would ban magazines holding more than 10 rounds of ammunition and place new security requirements on people who already own such weapons. It would also apply to semi-automatic rifles and handguns with fixed magazines capable of carrying more than 10 rounds, and all semi-automatic shotguns with folding or detachable stocks, pistol grips, forward grips or fixed magazines with room for more than five rounds.
It exempts assault weapons that are "lawfully possessed" as of the date the bill is enacted, but sales of exempted weapons would be subject to background checks.