Donald Trump has reiterated his call for a temporary ban on Muslims entering the United States in the wake of the Orlando massacre, but said it could be lifted once they were properly screened.
Gunman Omar Mateen — a New York-born Florida resident and US citizen who was the son of Afghan immigrants — was shot and killed by police early on Sunday morning after a three-hour siege, in which 49 people were killed.
The victims were enjoying a night out at gay club Pulse. The FBI and other agencies said investigators were poring over evidence inside the nightclub and in the closed-off streets around the scene of deadliest mass shooting in modern US history.
In a speech in Manchester, New Hampshire, that was intended to focus on rival Hillary Clinton, Mr Trump turned his focus to President Barack Obama and the threat of Islamic extremism through immigration.
"We must find out what is going on," the Republican presidential nominee said.
"We need to tell the truth about how radical Islam is coming to our shores."
Mr Trump then continued to suggest the Orlando massacre was the product of immigration from Afghanistan.
"The killer, whose name I will not use or ever say, was born to Afghan parents who immigrated to the United States," he said, adding that Mateen's father had formerly published support for the Taliban.
"Immigration from Afghanistan into the United States has increased nearly five-fold in just one year. If we want to remain a free and open society, then we have to control our borders."
Radicals, not Islam, to blame: Clinton
However Ms Clinton warned against demonising Muslim Americans.
Goaded by Mr Trump, Ms Clinton referred to Islamic State (IS) militants as "radical jihadists" after repeatedly refusing to go along with Republicans' description of the threat as "radical Islamic terrorism".
"The Orlando terrorist may be dead, but the virus that poisoned his mind remains very strong, and we must attack it," she said in a speech in Cleveland.
In proposals for dealing with threats of violence at home and abroad, the former US secretary of state called for increased efforts to remove IS propaganda from the internet, more air strikes in areas held by the group, and better coordination with allies in the region.
She specifically called out three US allies — Saudi Arabia, Qatar and Kuwait — for allowing their citizens to fund mosques and schools that train jihadists.
Mrs Clinton also proposed stricter gun control laws, reiterating previous calls to prohibit people on terrorism watch lists from buying firearms.
She pointed out that while the FBI was aware of Mateen as a possible threat, he was still able to purchase a gun legally.
She called for a complete ban on assault-style guns.
"It's important that we stop the terrorists from getting the tools they need to carry out the attacks, and that is especially true when it comes to assault weapons like those used in Orlando and San Bernardino," she said, drawing a standing ovation from the crowd.
Mateen 'an example of homegrown extremism': Obama
Mr Obama said there was no clear evidence the Orlando massacre was directed by a larger terrorist network, adding that the threat was "homegrown".
"As far as we can tell right now, this is certainly an example of the kind of homegrown extremism that all of us have been so concerned about for a very long time," the President told reporters in the Oval Office.
"It appears that the shooter was inspired by various extremist information that was disseminated over the internet.
Mateen had expressed allegiance to the radical Islamic State militant group, also known as ISIL and ISIS, in a call to the city's 911 emergency telephone line during a standoff with police while holding hostages in a gay nightclub called Pulse.
The president said he was concerned that the response to the massacre would turn into a debate over whether to toughen gun laws or pursue extremist militants like the Islamic State group.
"We have to go after these terrorist organisations and hit them hard," Mr Obama said.
"But we also have to make sure that it is not easy for somebody who decides they want to harm people in this country to be able to obtain weapons."