Republican presidential candidate Donald Trump has called for President Barack Obama to step down from his position after not linking the Orlando nightclub terror attack to 'Radical Islam'.

In a statement released following Obama's speech, he also said that Democratic presidential candidate Hillary Clinton should 'get out of this race for Presidency'.

Trump's comments come after 50 people were killed in a shooting at Pulse Nightclub in Orlando, Florida, early Sunday morning, marking the most deadly mass shooting in US history.

He said in his statement: 'Last night, our nation was attacked by a radical Islamic terrorist. It was the worst terrorist attack on our soil since 9/11, and the second of its kind in six months. My deepest sympathy and support goes out to the victims, the wounded, and their families.

'In his remarks today, President Obama disgracefully refused to even say the words "Radical Islam". For that reason alone, he should step down.

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The presumptive nominees for both parties, Hillary Clinton (left) and Donald Trump (right) initially reacted to this morning's shooting using Twitter

President Barack Obama pauses as he speaks about the massacre at an Orlando nightclub that claimed 50 lives during a news conference at the White House

Omar Mateen, 29, pictured above, had called 911 before he staged his attack which killed at least 50 people, and pledged allegiance to ISIS

'If Hillary Clinton, after this attack, still cannot say the two words 'Radical Islam' she should get out of this race for the Presidency.

'If we do not get tough and smart real fast, we are not going to have a country anymore. Because our leaders are weak, I said this was going to happen – and it is only going to get worse.

'I am trying to save lives and prevent the next terrorist attack. We can't afford to be politically correct anymore.'

Omar Mateen, 29, of Port St. Lucie in Florida, pledged allegiance to ISIS before opening fire at the Pulse gay club early on Sunday. He was eventually killed when police shot him dead inside the club three hours later.

Mateen was born in New York from parents who were from Afghanistan, though Trump still touted his controversial plans for a ban of all non-American Muslims coming into the United States.

He added: 'We need to protect all Americans, of all backgrounds and all beliefs, from Radical Islamic Terrorism - which has no place in an open and tolerant society.

'Radical Islam advocates hate for women, gays, Jews, Christians and all Americans. I am going to be a President for all Americans, and I am going to protect and defend all Americans. We are going to make America safe again and great again for everyone.'

President Obama pictured above speaking to the American people this afternoon. he said: 'We are still learning all the facts. This is an open investigation. We've reached no definitive judgment on the precise motivations of the killer'

Trump said that he will deliver a speech on Monday to further address the attack, immigration and national security.

Following the attack, Trump and Clinton initially took to Twitter to express their reactions to the mass shooting.

'Woke up to hear the devastating news from FL. As we wait for more information, my thoughts are with those affected by this horrific act,' Clinton wrote on Twitter, signing it with her trademark 'H' to show that the message was actually penned by the Democratic candidate.

In a statement made by her campaign later, Clinton also called for gun control.

Donald Trump suggested that many of his supporters were sending him 'congrats' for being right about radical Islamic terrorism, but he said it's not 'congrats' that he wants

Hillary Clinton reacted to the news of the Orlando shooting via Twitter, with her tweet then translated into Spanish, calling it 'devastating'

Donald Trump initially just let his readership know about the Orlando shooting and then went back to attacking Hillary Clinton on Twitter

Trump took to Twitter writing: 'Horrific incident in FL. Praying for all the victims & their families. When will this stop? When will we get tough, smart & vigilant?'

'This is the deadliest mass shooting in the history of the United States and it reminds us once more that weapons of war have no place on our streets,' Clinton said.

Trump made Twitter followers aware of the shooting, then went back to attacking Clinton - this time for a new general election ad - before penning more tweets about the tragedy in Orlando, in which a gunman entered a gay nightclub and mowed down 50 people, with another 53 left injured.

'Appreciate the congrats for being right on radical Islamic terrorism, I don't want congrats, I want toughness & vigilance. We must be smart!' Trump wrote.

He later released the statement that called for Clinton and Obama to step down from their respective roles.

Trump's initial reaction was to tweet that there was a 'really bad shooting in Orlando.'

'Police investigating possible terrorism. Many people dead and wounded.'

He then turned his attention to Clinton's new ad, which shows Trump saying he'd like to 'knock the crap out' of a protester.

It also shows The Donald mocking a disabled New York Times Reporter. Trump countered that that's not what was really happening.

'Clinton made a false ad about me where I was imitating a reporter GROVELING after he changed his story. I would NEVER mock disabled. Shame!' he wrote, initially misspelling the word 'mock.'

Trump then addressed the shooting again.

'Horrific incident in FL. Praying for all the victims & their families. When will this stop? When will we get tough, smart & vigilant?' Trump wrote.

The Republican has often talked about taking on 'radical Islamic terrorism,' and early reporting points to the gunman, 29-year-old Omar Mateen of Port St. Lucie, Florida, having 'leanings to radical Islamic terrorism,' according to the FBI.

He then updated his response several hours later asking 'when will we get tough, smart & vigilant?' and calling the shooting a 'horrific incident'

Donald Trump dared President Obama to use the term 'radical Islamic terrorism' in his remarks to the American public. The president did not

In his third tweet, Trump noted that he was being heralded by supporters for being 'right' on radical Islamic terrorism, but said he would prefer 'toughness' over compliments.

In a fourth tweet, Trump challenged President Barack Obama to call the attack 'radical Islamic terrorism.'

'Is President Obama going to finally mention the words radical Islamic terrorism? If he doesn't he should immediately resign in disgrace!' Trump tweeted.

When President Obama appeared in the briefing room and spoke, he labeled the massacre both an 'act of terror' and an 'act of hate.'

The president did not bring Islam into it, though made a veiled call for gun control, saying, 'to actively do nothing is a decision as well,' the president added.

Aerial view on Sunday of the mass shooting scene at the Pulse nightclub in Orlando. The three-hour rampage killed at least 50 people

FBI agents investigate near the damaged rear wall of the Pulse Nightclub where Omar Mateen gunned down 50 people

After Obama's address, Trump resumed his Twitter presence, passing along reports he had seen in the media.

'Reporting that Orlando killer shouted 'Allah hu Akbar!' as he slaughtered clubgoers. 2nd man arrested in LA with rifles near Gay parade,' Trump wrote.

He also retweeted a comment from a supporter who said, 'please make us safe. We cannot have Hillary as president. We will be in so much trouble.'

Trump didn't mention the gay community in any of his responses, except to note that there was a second incident in Los Angeles, in which a man was discovered with explosives and guns wanting to target the city's Pride parade.

Victims and witnesses make their way out of the Orlando Police headquarters building as FBI and Orlando police department and the Orange County sheriff's office investigate the terror attack at the Pulse nightclub

Sen Bernie Sanders, who will compete in one final Democratic primary this Tuesday in Washington, DC, was the first of the presidential candidates to bring up gun control, with Clinton not making her full statement until mid-afternoon.

'It's horrific, it's unthinkable,' Sanders said this morning, as he appeared on several of the Sunday shows. 'And just hopes go out to all those who were shot that they can recover.'

'We should not be selling automatic weapons which are designed to kill people,' Sanders continued.

'We have got to do everything that we can on top of that to make sure that guns do not fall into the hands of people who should not have them, criminals, people who are mentally ill,' the Vermont senator added.

A member of the Medical Examiners office wheels a body to a vehicle from the mass shooting at Pulse Nightclub

A mini van outside the Pulse nightclub in Orlando which is believed to have been used by the shooter

Donald Trump doubled down on his plans to ban non-American Muslims from entering the United States despite the fact that the shooter was an American

Later, in a statement from his campaign, he expanded his comments, making sure to mention the LGBT community, which was specifically targeted in this attack.

'All Americans are horrified, disgusted and saddened by the horrific atrocity in Orlando,' Sanders said.

'At this point we do not know whether this was an act of terrorism, a terrible hate crime against gay people or the act of a very sick person, but we extend our heartfelt condolences to the victims' families and loved ones and our thoughts are with the injured and the entire Orlando LGBTQ community,' Sanders said.

Terry DeCarlo, executive director of The LGBT Center (Gay, Lesbian, Bisexual, Transgender Community) of central Florida on North Mills cries near the scene of the Pulse nightclub terror attack

Marco Rubio, a presidential contender until mid-March who remains a Florida senator, talked at length about radical Islam when speaking to reporters live from Orlando.

'We know that some of it is inspired by a warped ideology,' Rubio said. 'We know that we've been in conflict with it for a very long time.'

'We know that they seek to intimidate us, they seek to terrorize us, and I hope they see today that they won't terrorize Americans, they won't terrorize Floridians,' Rubio continued.

'That we stand for and with all Americans, irrespective of their sexual orientation, irrespective of their party ideology, irrespective of where they live,' the Florida senator noted.

Clinton, several hours after the attack, tweeted more support for the LGBT community.

'Please know that you have millions of allies across our country. I am one of them,' Clinton tweeted.

She and President Obama also called off their first appearance together on the campaign trail this week.

Clinton and Obama were going to officially join forces on Wednesday at an event in Wisconsin.

It has now been indefinitely postponed.