WASHINGTON/ORLANDO - President Barack Obama and Democratic presidential candidate Hillary Clinton launched nearly simultaneous attacks on Donald Trump on Tuesday, heaping scorn on the presumptive Republican presidential nominee for his proposed Muslim ban.

Clearly angered, Obama used a speech at the Treasury Department for an extraordinary rejection of Trump's proposed suspension of immigration from countries with a "history of terrorism" in response to the Orlando, Florida, nightclub massacre.

The Democratic president, without mentioning Trump by name, dismissed the Republican's criticism that Obama does not employ the term "radical Islamic terrorism" to describe Islamic State militancy. Obama called it a political distraction. "What exactly would using this label accomplish, what exactly would it change?" Obama said. "Someone seriously thinks we don't know who we're fighting? ... There's no magic to the phrase radical Islam. It's a political talking point."

An angry President Barack Obama Tuesday lashed out at Republicans, and particularly Donald Trump, who have called him soft on terrorism, warning that "loose talk" about Muslims has harmed the United States' campaign against militant groups in the Middle East and elsewhere. He said the anti-Islam rhetoric from Trump, the presumptive Republican presidential nominee, is "not the America we want."

Obama is argued that treating Muslim-Americans differently won't make the US safer. He says it will make the country less safe by fuelling the notion among followers of the Islamic State group that the West hates Muslims. In this regard, Obama doubled down on his proposal to temporarily ban foreign Muslims from entering the US.

Obama says the US was founded on freedom of religion and that there are no religious tests in America. He says such talk makes Muslim-Americans feel like their government is betraying them.

Clinton, speaking to supporters in Pittsburgh, said Trump's proposal bolstered her case that Trump is temperamentally unfit to serve as president, saying the commander-in-chief "is a job that demands a calm, collected and dignified response" to events like the Orlando massacre early on Sunday.

She noted that Trump seemed to suggest on Monday in a television interview on Monday that Obama might have somehow been responsible for the deadliest mass shooting in modern US history, a point that Trump said he did not make.

Meanwhile, the gunman who massacred 49 people at the Pulse club in Orlando was himself a regular at the gay nightspot, four clubgoers told the Orlando Sentinel.

"Sometimes he would go over in the corner and sit and drink by himself, and other times he would get so drunk he was loud and belligerent," Ty Smith told the Sentinel, referring to slain shooter Omar Mateen, 29.

Smith told the paper that he saw Mateen inside at least a dozen times. "We didn't really talk to him a lot, but I remember him saying things about his dad at times," Smith said. "He told us he had a wife and child."

Another Pulse regular, Kevin West, told the Los Angeles Times that Mateen messaged him on and off for a year using a gay chat app.

When Omar Mateen met with his father the day before he killed 49 people in a siege of a gay nightclub, he betrayed nothing of the rage that would erupt into the worst mass shooting in modern American history. "I didn't notice anything wrong," Seddique Mateen said in an interview. "He was very slick."

At the Islamic Center of Fort Pierce, a mosque he attended for nearly a decade, Mateen occasionally prayed with Moner Mohammad Abu-Salha, a 22-year-old Palestinian-American who in 2014 became the first American suicide bomber in Syria, although they "did not interact with each other," said Adel Nefzi, a mosque board member.

Meanwhile, Saudi Arabia's King Salman has condemned the killing of 49 people at a gay nightclub in Florida, official media said on Tuesday.

"We received with great regret the news of the armed terrorist attack in Florida and the resulting casualties and victims," Salman said in a message of condolence to US President Barack Obama.

"We condemn and denounce this disgraceful criminal act which is not accepted by religion or international norms and conventions."

The Islamic State group, which has also claimed attacks within Saudi Arabia, said gunman Omar Mateen acted as one of its "soldiers" in Sunday's rampage in Orlando.

But FBI chief James Comey said there was no indication of a plot directed from outside the United States, and he was confident the gunman had been "radicalised" while consuming online propaganda.

Saudi Arabia's interior ministry said Mateen had twice travelled to the kingdom to perform the umrah pilgrimage, in 2011 and 2012.

Saudi Arabia has repeatedly denounced bombings and shootings carried out in various countries by IS and other extremists. It has also been accused of fostering extremism.

Hillary Clinton, the presumptive Democratic party nominee for US president, on Monday accused Saudi Arabia and its neighbours of allowing radicalism to thrive.

"It is long past time for the Saudis, the Qataris, and the Kuwaitis and others to stop their citizens from funding extremist organisations," Clinton said in a speech.

"And they should stop supporting radical schools and mosques around the world that have set too many young people on a path toward extremism."

In his message, Salman stressed "the importance of the concerted efforts of the international community to respond to all acts of violence and terrorism".

His son, the powerful Deputy Crown Prince Mohammed bin Salman who is currently on an official visit to the United States, also sent condolences.