Presidential hopeful Donald Trump\u00a0on Wednesday\u00a0said he will meet with the leading U.S. gun rights group about preventing people on a government terrorism "watch list" from buying guns, as some fellow Republicans considered new gun restrictions following the Orlando massacre. The long-simmering issue of gun control gained new urgency after a man who had been on one of the terrorism watch lists killed 49 people at an Orlando gay nightclub early\u00a0on Sunday. The National Rifle Association, a politically influential lobbying group that claims more than 4 million members and has worked with congressional Republicans in thwarting gun control legislation, said in a statement it was "happy to meet" with Trump, who it endorsed for president on May 20. Also Read:\u00a0US senators, Donald Trump open to ban on some gun sales after Orlando shootings But Chris Cox, executive director of the NRA's Institute for Legislative Action, said the group's position on the issue of barring people on the watch lists from buying guns "has not changed." On Tuesday, the NRA said on Twitter that barring people on watch lists from buying guns is "ineffective, unconstitutional, or both." Senator John Cornyn, the No. 2 Senate Republican, and Democratic Senator Dianne Feinstein were holding private talks on a possible compromise bill on stopping weapons sales to those on watch lists, according to a Cornyn aide. Another Republican, U.S. Senator Pat Toomey of Pennsylvania, also is working on a bill that would keep guns from people on watch lists, a gun control group said. Republicans have staunchly defended gun rights and fought off attempts during Democrat Barack Obama's presidency to implement new restrictions. But Republican opponents of gun control measures are again under pressure after the Orlando killings. "I will be meeting with the NRA, who has endorsed me, about not allowing people on the terrorist watch list, or the no fly list, to buy guns," Trump wrote on Twitter. 'THOROUGHLY INVESTIGATED' The FBI maintains two terrorism "watch lists," a smaller "no fly" list barring people from flying to and from the United States and a larger one that subjects travelers to greater scrutiny at airports and border crossings. The Orlando gunman, Omar Mateen, the U.S.-born son of Afghan immigrants, was on the broader list at one time. The NRA's Cox said in a statement that "anyone on a terror watchlist who tries to buy a gun should be thoroughly investigated by the FBI and the sale delayed while the investigation is ongoing." Cox added that "the NRA believes that terrorists should not be allowed to purchase or possess firearms," but his statement did not define who he considered to be terrorists or specify whether that included those on the watch lists. Cox separately appears on the NRA's website saying, "Gun laws don't deter terrorists." Cox also voiced backing for legislation offered in December by Cornyn, who proposed to put gun sales on hold for 72 hours for people on watch lists. Critics have said such background checks could take longer to complete. Cornyn's proposal was in response to Democratic legislation to ban the sale of weapons and explosives to people on the watch lists. Republicans blocked that legislation, arguing that innocent people are often placed on watch lists and the bill would deny them their constitutional rights to buy guns. Republican Senate Majority Leader Mitch McConnell said\u00a0on Tuesday\u00a0that "nobody wants terrorists to have firearms" and that he was open to suggestions from experts on legislation that could address the problem. White House spokesman Josh Earnest said it was too soon to tell if Republicans would support "common sense" steps like blocking firearm sales to people on the "no fly" lists. Trump, the presumptive Republican presidential nominee, last month told an NRA convention that he would protect the constitutional right to bear arms. He accused the presumptive Democratic nominee, Hillary Clinton, of wanting to abolish that right, which she says is false. Trump said in a November television interview he would support gun restrictions for someone on a "watch list" who is "an enemy of state." The Trump campaign declined to provide more information about the NRA meeting. "We will send details at the appropriate time," campaign spokeswoman Hope Hicks said.