"There are numerous rules that were broken. That's not the way a democracy works and I think you will see appropriate measure taken in the very near future," McCarthy told reporters in the Capitol, adding, "Are you going to let the House stand with that behavior going forward? I think it would create real damage to the reputation of the House in the long term."
House Republican leaders are discussing several options as potential penalties, including voting on a resolution that condemns the sit-in or leveling fines for rule violations, according to a senior GOP leadership aide familiar with the discussions.
During the protest in June, dozens of House Democrats sat on the floor in the well, chanted and yelled when Republicans attempted to move onto legislative business, actions which are breaches of floor decorum.
House Rules include specific parameters for when a member can speak, and whom they can address from the podium in the front of the chamber.
Rep. John Lewis, D-Georgia, the civil rights icon who was beaten by police in the 1965 march in Selma, Alabama, was one of the leaders of the effort, which gained national attention. Democrats demanded that the House vote on a bill that would deny gun sales to individuals on a government "no fly list" designed to flag potential threats to airlines. They also urged action on legislation requiring background checks for gun purchases.
Several Democrats involved in the protest also used mobile phones to broadcast their demonstration using streaming social media apps after the official cameras that film floor business, which are controlled by the GOP majority, were turned off when the chamber went into recess.
Despite the high-profile protest, Democrats failed to secure votes on any gun measures.
After the episode, which forced GOP leaders to abruptly cancel business for the week and start a scheduled recess early, House Speaker Paul Ryan said he was troubled by the precedent it set and told reporters that he and other leaders were investigating with administrators and considering what type of penalties they might impose.
McCarthy said Tuesday he has spoken with several Democrats about the episode and that they admitted they broke rules and understood there would be consequences.
Rep Steny Hoyer, D-Maryland, the No. 2 House Democrat, told CNN he hadn't spoken with any GOP leader, or heard from any Democrat who had, but defended the sit-in.
"Almost every member thinks to themselves we made a point that we need to consider bipartisan legislation sponsored by (GOP Rep. Peter King) that 80% of the America wants," he told CNN.
And Hoyer welcomed any punitive moves, saying, "If you want to censure for that, then go to it."
House Minority Leader Nancy Pelosi voiced similar sentiment on any possible punishment in July, quipping about potential penalties threatened by Ryan or other Republicans, "Make my day. Make my day."