By Susan Cornwell and David Morgan

WASHINGTON (Reuters) - A divided Republican Party on Wednesday fought over gun control legislation that was cobbled together following last month's mass shooting in Orlando, raising questions over U.S. House Speaker Paul Ryan's ability to get the measure passed.

While Democrats have said the gun control proposal put forward by Republican leaders was too weak, an influential group of approximately 40 conservative House Republicans announced their opposition as well, saying the plan did not do enough to protect gun buyers.

The legislation fails "to do enough to address the threat of radical Islamic terrorism," according to a statement by the conservative Freedom Caucus. The group also complained of "the inclusion of gun control provisions that fail to adequately protect due process."

With the Republican leadership's legislation under attack from both liberals and conservatives, it was unclear whether Ryan could muster the 218 votes he would need for passage in the House of Representatives.

Last month, the Senate failed to approve any of several competing Republican and Democratic gun control proposals offered in the wake of the June 12 shooting at a gay night club in Orlando that killed 49 and injured 53 others.

During the Senate debate, Democratic lawmakers staged a sit-in on the House floor to pressure Republican leaders to pass legislation expanding background checks on gun sales and blocking gun purchases by people on terrorism watch lists.

The Republican leadership bill, announced last Friday, would give the government three days to convince a judge that a gun sale should be blocked. Ryan said Wednesday that he intended to bring it to the floor for a vote this week or next, but also noted changes were being sought by numerous lawmakers.

"The last thing we're going to do is rush something to the floor that we don't have right," Ryan said.

Representative Matt Salmon of Arizona, a Freedom Caucus member, said he objected to Ryan pushing the bill without allowing it to be processed by relevant committees first.

Salmon said that Ryan told House Republicans in a closed meeting that he was rushing the legislation to the House floor because "there are members that need to have this vote" for political reasons in swing districts that could go either Republican or Democratic in the Nov. 8 elections.

Democrats, meanwhile, continued to pressure Ryan for votes on their more sweeping gun control measures.

Representative John Larson of Connecticut, a ringleader of the Democrats' sit-in, said his fellow Democrats plan to support Republican mental health legislation that could help avert some mass shootings. Larson added he hoped it would be seen as an olive branch to Republicans toward progress on gun control.

Scores of gun control advocates demonstrated outside the House chamber in sweltering heat on Wednesday morning, as 91 people wearing orange t-shirts stood on the steps leading to the House demanding action.

They represented the 91 people who, according to government statistics, die each day in the United States from gun violence. Many of them die as a result of suicide.

(Reporting by David Morgan, Susan Cornwell and Richard Cowan; Editing by James Dalgleish)