By David Morgan and Susan Cornwell

WASHINGTON (Reuters) - U.S. congressional Republican leaders on Tuesday resisted Democratic demands for a vote on gun-control measures and warned that some could face punishment for an unusual sit-in last month that tied up the House of Representatives for 25 hours.

With Democrats already rejecting a Republican gun bill and warning of possible further protests, the House appeared to be heading for renewed discord over gun restrictions in the aftermath of the June 12 mass shooting at a gay nightclub in Orlando, Florida, in which 49 people were gunned down.

Hours before he was due to discuss gun legislation with two Democratic lawmakers who led the sit-in, House Speaker Paul Ryan said he believed their proposals would violate the U.S. Constitution and warned that he would not "incentivize" more disruptive behavior.

"The last thing we are going to do is surrender the floor over to these kinds of tactics when we know it's going to compromise the constitutional rights of law-abiding citizens," Ryan said in an interview with radio station WTMJ in Milwaukee.

At a press briefing, House Republican Majority Leader Kevin McCarthy said he and Ryan would also meet with the chamber's top enforcement official this week to talk about reports that some Democrats at the June 22-23 sit-in engaged in "intimidation" while carrying out their protest over Republican efforts to stop it.

"That behavior cannot continue onto the floor," McCarthy said.

Ryan has announced that the House will vote this week on counter-terrorism legislation that includes a measure intended to keep guns out of the hands of people the government suspects of involvement in violent extremism. But Democrats say the Republican measure is inadequate because authorities would have only three days to convince a judge that a gun sale should be blocked.

"Ninety-one people die each day from gun violence in this country and the best Speaker Ryan can muster is a meaningless bill," said House Democratic leader Nancy Pelosi aide Drew Hammill.

Two weeks ago, scores of Democrats flooded the House chamber, sitting on the floor and chanting to demand action on two measures: one that would allow the government to block gun sales to suspected extremists without first getting a judge's approval, and another that would expand background checks to gun shows and other venues.

McCarthy said Republicans are now gathering facts on the sit-in and will decide whether to seek punishment.

"That was not a behavior becoming of the United States Congress," he told reporters.

(Reporting by David Morgan; Editing by Andy Sullivan and James Dalgleish)