WASHINGTON — As Democrats make an aggressive push for new gun control legislation, they have made a calculated decision to stop short of pursuing their most ambitious goal: an assault weapons ban.

The overwhelming majority of House Democrats — 211, seven shy of the 218 needed for passage — are co-sponsoring legislation to ban military-style semiautomatic weapons, similar to the ban in effect from 1994 to 2004. But some centrist Democrats remain skittish about any proposal that keeps firearms from law-abiding citizens — a frequent charge against Democrats by Republicans and gun rights groups — making any such ban politically risky for moderates in Trump-friendly districts. In the Senate, it draws less support.

The split reveals just how complicated gun politics remain inside the Democratic Party, even as mass shootings are terrorizing the nation and the Twitter hashtag #DoSomething has captured the mounting public demands for Congress to act.

On the presidential campaign trail, Democrats like former Vice President Joseph R. Biden Jr. are rallying behind an assault weapons ban, and Beto O’Rourke, the former congressman from Texas, has gone so far as to call for a mandatory government program to buy back the weapons of war. But on Capitol Hill, Speaker Nancy Pelosi and Senator Chuck Schumer of New York, the Democratic leader, have barely breathed a word about reviving the ban.