By David Morgan and Richard Cowan

WASHINGTON (Reuters) - Prospects dimmed on Monday for the U.S. House of Representatives to vote this week on Republican legislation to restrict gun sales to suspected extremists before Congress goes on a seven-week summer break.

Republicans including House Speaker Paul Ryan have been under pressure to act on gun legislation since the June 12 mass shootings at a gay nightclub in Orlando, Florida. Congress begins a summer recess on Friday.

But with the House floor schedule filling with other bills, Republicans said gun legislation was unlikely to come up before September, when prospects for serious action could be overshadowed by the fall presidential election campaign.

Representative Jim Jordan of Ohio, who heads the conservative House Freedom Caucus, said, "I do not anticipate that bill."

The measure, backed by the National Rifle Association, would give government authorities three days to convince a judge to block the sale of weapons to someone suspected of involvement in violent extremism.

But Ryan has been unable to win support from conservative Republicans who say the measure poses potential constitutional problems and should be subjected to regular legislative channels including formal hearings.

Republican lawmakers say discussions aimed at finding compromise are continuing. But the measure did not come up at a Monday meeting with Republican leaders to discuss the week's agenda, said another lawmaker who predicted it would not see a vote this week.

The stalemate leaves hanging Democratic demands for stronger gun restrictions, despite an unprecedented 25-hour sit-in by House Democrats last month, and sidelines any potential movement on an alternative bipartisan bill seen as a possible compromise.

"A vote is going to be stalled" until Congress returns from its long summer break, one Republican aide said.

Lawmakers initially believed Congress could pass some kind of measure before their summer recess after the Orlando shootings raised national security concerns and polls showed a majority of Americans in favor of greater restrictions.

(Reporting by David Morgan and Richard Cowan; Editing by Cynthia Osterman)