New Jersey Sen. Frank Lautenberg and New York Rep. Carolyn McCarthy said Tuesday that they have introduced companion bills to ban high-capacity magazines holding more than 10 rounds of ammunition.

The proposal from the two Democrats is part of a broad set of gun controls President Obama has vowed to push for in his second term, following the shooting deaths of 20 children and six adults at Sandy Hook Elementary School in Newtown, Conn., last month.

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“It is clearer than ever that there is no place in our communities for military-style supersized magazines like those used inside Sandy Hook Elementary School, in Aurora, and in Tucson, and I will keep working to reinstate the ban on them,” said Mr. Lautenberg.

His bill has attracted 16 Democratic co-sponsors, including Sen. Dianne Feinstein of California, who is planning to roll out a ban on military-style, so-called assault weapons on Thursday. He first introduced the bill in 2011 after a deranged gunman killed six people and wounded 13 others, including former Rep. Gabrielle Giffords, at a Tucson shopping center.

Ms. McCarthy, a Democrat from New York, called high-capacity magazines “the common thread in every mass shooting in recent history.” Her husband was killed in a shooting spree on the Long Island Rail Road in 1993.