Republican presidential candidate Donald Trump says he will meet with the country's leading gun-rights group about keeping people on a government terrorism watch list from buying guns.
It is a marked break with Republican Party orthodoxy, which typically opposes any restrictions on firearm ownership.
There have been growing calls for restrictions on buying guns in the United States after a gunman killed 49 people at an Orlando, Florida, nightclub last weekend.
It has emerged the gunman was legally able to buy an assault rifle even though the FBI had investigated him in the past for possible ties to militant groups.
Democratic presidential candidate Hillary Clinton has supported stricter gun laws.
She is pushing for new legislation which would prevent people on the FBI's no-fly terrorism watch list from buying firearms.
"Surely, we can agree, if the FBI is watching you for suspected terrorist links, you should not be able to buy a gun with no questions asked."
Congressional Republicans have previously blocked a Democratic effort to restrict gun sales to people on the watch list.
House Democratic Caucus chairman Xavier Becerra says it is time for Republicans to act now.
"This Congress should not leave this week without giving us a vote on something very simple: no fly, no buy. If you can't fly because you're on a watchlist by our government, and you are not allowed on an airplane, you should not be allowed to enter a gun shop and walk out with an assault weapon."
President Barack Obama has called for what he calls common-sense gun reforms.
He includes the reintroduction of a ban on assault weapons that expired 12 years ago.
"Enough talking about being tough on terrorism. Actually be tough on terrorism, and stop making it (as) easy as possible for terrorists to buy assault weapons. Reinstate the assault-weapons ban."
Meanwhile, presumptive Republican presidential candidate Donald Trump has suggested there may have been fewer victims in the Orlando attack if nightclubbers had had guns.
"If the bullets had been going in the other direction, you would have had a situation, folks, that would have been always horrible but nothing like the carnage that we all, as a people, suffered this weekend."
Mr Trump later said in a tweet he would meet with the politically influential National Rifle Association (NRA) about preventing people on the watch list from buying guns.
Mr Trump has the endorsement of the powerful group, which claims more than 4 million members and has worked with congressional Republicans to thwart gun-control legislation.
The NRA has responded it is happy to meet with Mr Trump.
It has restated its position that anyone on a terrorism watch list who tries to buy a gun should be thoroughly investigated by the F-B-I and the sale delayed.
The NRA says, if evidence of terrorist activity is uncovered, the government should be allowed to go to court and block the sale.
At the same time, it says Americans wrongly put on a watchlist should be removed.
Meanwhile in Sydney a special commemoration service was held at Saint Andrews Cathedral for the victims of the Orlando attack.
The Anglican Archbishop of Sydney, Dr Glenn Davies, was among those to address the gathering.
"It is a loss for the LBGTI community. It is a loss for the American people. It is a loss for us in Australia. It is a loss for all humanity."
Members of the public were united behind the victims and their families.
"Oh, I just feel for them, I really do. It's a dreadful way to lose your kids and your loved ones."
"Everyone needs compassion and grace at the moment, and we need healing and hope."
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