WASHINGTON — Representative Kevin McCarthy, the House majority leader, said Tuesday that Democrats who essentially seized the House floor last month to protest the lack of votes on gun legislation might be punished for breaking House rules.

The behavior was not “becoming of the U.S. Congress,” Mr. McCarthy told reporters. He said he had been told that Democrats had mistreated House staff members and had perhaps even damaged congressional furniture during their sit-in-style protest.

Mr. McCarthy said that he and the House speaker, Paul D. Ryan, would soon meet with the House sergeant-at-arms to discuss investigative paths and possible ramifications for the Democrats.

“This is not the way the House should work,” Mr. McCarthy said. “You first have to know all the facts. Action has to be taken on behavior taken toward professional staff.”