By David Morgan and Susan Cornwell

WASHINGTON (Reuters) - U.S. congressional Republicans 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 further protests, the Republican-controlled House appeared to be heading for renewed discord over gun restrictions following the June 12 mass shooting at a gay nightclub in Orlando, Florida.

House Speaker Paul Ryan met for about 30 minutes on Tuesday with two Democrats who led the sit-in: Representatives John Lewis of Georgia and John Larson of Connecticut. The Democrats said they would ask Ryan for a vote on two Democratic-backed measures but left the meeting without speaking to reporters.

"The path ahead ... will be discussed and determined by the majority in the coming days," Ryan spokeswoman AshLee Strong said later in a statement.

The measures sought by Democrats would expand background checks for gun purchases and allow the government to block gun sales to suspected extremists without first getting a judge's approval.

Hours before the meeting, Ryan suggested a vote on the Democratic legislation was unlikely, telling a Milwaukee radio station: "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."

House Republican leader Kevin McCarthy said separately that he and Ryan would meet this week with the chamber's top enforcement official to talk about reports that some Democrats at the June 22-23 sit-in engaged in "intimidation" while carrying out their protest.

Ryan has announced that the House will vote this week on a measure intended to keep guns out of the hands of people the government suspects of involvement in violent extremism. But Democrats say the legislation 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.

Six people who said they lost family and loved ones to gun violence were arrested in the U.S. Capitol on Tuesday, after a protest demanding Congress reject the Ryan measure and vote on the Democratic measures.

(Reporting by David Morgan; Editing by James Dalgleish and Peter Cooney)