By David Morgan

WASHINGTON (Reuters) - Republicans in the U.S. House of Representatives on Friday introduced a measure intended to prevent gun sales to people on government watch lists, only to draw demands from Democrats for stronger proposals and a warning of possible new protests.

A week after Democrats ended a 25-hour sit-in on the House floor to call for gun legislation after the June 12 mass shooting in Orlando, House Majority Leader Kevin McCarthy, a Republican, said lawmakers will vote next week on a measure giving government authorities three days to convince a judge that someone on a terrorism watch list should not be allowed to obtain a firearm.

"It is a responsible measure that confronts this threat while protecting the rights of law-abiding citizens," House Speaker Paul Ryan said in a statement.

But in a Friday conference call, House Democrats reached "a clear consensus" to oppose the measure, calling it the handiwork of the National Rifle Association, an aide said. Similar legislation, backed by the NRA, was blocked by Democrats in the Senate last week.

Democrats also called for two amendments: one to allow the U.S. attorney general to decide without court approval whether someone on a watch list could buy a gun; and another to expand existing background checks to all commercial gun sales including those at guns shows.

Democratic Representative John Lewis of Georgia and John Larson of Connecticut, who led last week's sit-in, asked for a meeting with Ryan to request votes on the amendments, which consist of legislation originally sponsored by Republican Peter King of New York. Ryan agreed to meet with the Democrats on Tuesday to discuss the matter, a House Democratic aide said.

"If these amendments are not allowed, then members will have further discussions about possible actions to take in response to this refusal to allow a vote on commonsense gun legislation," said another House Democratic aide.

The new Republican proposal, which would apply to anyone who has been suspected of violent extremism within the past five years, would require authorities to show probable cause that a would-be buyer "will commit an act of terrorism" or violates existing prohibitions on undocumented immigrants, fugitives, convicts and people with mental illness.

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The gun provisions were tucked into a bill aimed at stepping up efforts against terrorism, including what the legislation referred to as "radical Islamist terrorism".

Some Republicans have criticized Democrats for avoiding such terms to describe events like the Orlando, Florida shooting where a gunman pledging allegiance to the Islamic State killed 49 people last month.

Republican presidential candidate Donald Trump said recently that President Obama should resign for not having used "radical Islam" in a statement responding to the Orlando massacre, in which police identified the shooter as a U.S. citizen born in New York to Afghan immigrants.

The NRA said it was reviewing the legislation, while the Brady Campaign to Prevent Gun Violence said the legislation proposed by House Republicans was a publicity stunt.

(Reporting by David Morgan; Additional reporting by Susan Cornwell; Editing by Matthew Lewis and James Dalgleish)