The day after a shooting at an Orlando nightclub, Republican presidential candidate Donald Trump railed against the president and warned that Muslims should be banned from entering the US, while Democratic rival Hillary Clinton called for changes to gun restrictions.

"Look, we're led by a man that either is not tough, not smart, or he's got something else in mind," Trump said in a lengthy interview on Fox News early yesterday morning.

"And the something else in mind -- you know, people can't believe it. People cannot, they cannot believe that President Obama is acting the way he acts and can't even mention the words 'radical Islamic terrorism.' There's something going on. It's inconceivable. There's something going on."

In that same interview, Trump was asked to explain why he called for Obama to resign in light of the shooting and he answered, in part: "He doesn't get it or he gets it better than anybody understands -- it's one or the other and either one is unacceptable."

After the deadly shooting in an Orlando nightclub on June 12, some in politics pushed for stricter gun control while others asked for prayers. GOP presidential candidate Donald Trump ignited controversy with his tweets.

Obama said yesterday there was no evidence that the massacre in a Florida nightclub was directed from abroad or was part of a larger plot.

After being briefed on America's most deadly mass shooting in modern times by top security aides, Obama said "we don't yet know" the shooter's motivations.

Obama called the shooting a case of “homegrown extremism” Monday, saying that the gunman appeared to be “inspired by various extremist information that was disseminated over the Internet.”

"At this stage we see no clear evidence that he was directed externally," Obama said.

"It does appear that at the last minute he announced allegiance to ISIL, but there is no evidence so far that he was in fact directed by them," he said, using an acronym for the Islamic State group.

"There's also no direct evidence that he was part of a larger plot."

IS earlier claimed responsibility for the massacre, saying in a radio bulletin that it was carried out by "one of the soldiers of the caliphate."

Trump on Sunday had called for Obama to resign for not using the words "radical Islam" in his comments about the shooting. He also renewed his call for a temporary ban on Muslims entering the United States.

During an appearance on the "Today" show later yesterday morning, Savannah Guthrie pushed Trump to explain what he meant in the earlier interview.

"Well there are a lot of people that think maybe he doesn't want to get it," Trump said. "A lot of people think maybe he doesn't want to know about it. I happen to think that he just doesn't know what he's doing, but there are many people that think maybe he doesn't want to get it. He doesn't want to see what's really happening. And that could be."

Guthrie asked Trump why that would be, and the presumptive Republican presidential nominee responded: "Because Savannah, Savannah, why isn't he addressing the issue? He's not addressing the issue. He's not calling it what it is. This is radical Islamic terrorism. This isn't fighting Germany; this isn't fighting Japan, where they wear uniforms."

Trump seemed to repeatedly accuse Obama yesterday of identifying with radicalised Muslims who have carried out terrorist attacks in the United States and being complicit in the mass shooting.

"We have many people coming in whose hate is equal to his and just as bad and even worse, frankly, and we have to stop people from coming in," Trump said, adding that gun control measures also could not stop a terrorist attack.

"The problem was that we have a maniac, we have a madman. He could have used a bomb. He could have used other things, just as easily, just as easily," Trump said. "It would have been, probably, even more devastating. So that's not the problem."

Trump has repeatedly taken credit for having been "right" on issues of terror, and yesterday he continued to face scrutiny for a tweet he posted on Sunday that read: "Appreciate the congrats for being right on radical Islamic terrorism, I don't want congrats, I want toughness & vigilance. We must be smart!"

"I'm getting thousands of letters and tweets that I was right about the whole situation," Trump said on Fox News. "I mean, I've been right about a lot of things, frankly... I was right about many, many things."

HILLARY ON GUN CONTROL

Hillary Clinton yesterday warned against demonising Muslim Americans.

In proposals for dealing with threats of violence at home and abroad, Hillary called for increased efforts to remove Islamic State propaganda from the Internet, more air strikes in the areas held by the militant group and better coordination with allies in the region.

She specifically called out three US allies - Saudi Arabia, Qatar and Kuwait - for allowing its citizens to fund mosques and schools that train jihadists.

She also called for stricter gun control laws, reiterating prior calls to prohibit those on terrorism watch lists from buying guns. She pointed out that while the Federal Bureau of Investigation was aware of Mateen as a possible threat, he was still able to legally purchase a gun.

[From Washington Post, Reuters, AFP]