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Donald Trump has promised to "straighten out" the world, in a chilling Washington DC speech.

And he said people shouldn't worry about "tough phone calls" he's had with world leaders - including one where he threatened to send US troops into Mexico.

Speaking to the National Prayer Breakfast - a meeting of religious leaders in the capital - he declared the world to be "in trouble".

Last night it was reported Trump had virtually threatened to invade Mexico in his first call with President Enrique Peña Nieto.

In today's speech, he said: "The world is in trouble, but we’re going to straighten it out, OK? That’s what I do. I fix things. We’re going to straighten it out.

"Believe me. When you hear about the tough phone calls I’m having, don’t worry about it. Just don’t worry about it. They’re tough.

(Image: REUTERS)

"They have to be tough. It’s time we’re going to be a little tough folks. We’re taken advantage of by every nation in the world virtually. It’s not going to happen any more."

In his phone call with the Mexican President, Trump is reported to have said: "You have a bunch of bad hombres down there.

"You aren't doing enough to stop them. I think your military is scared. Our military isn't, so I just might send them down to take care of it."

A White House official said today: "Reports that the President threatened to invade Mexico are false. Even the Mexican government is disputing these reports."

He was also reported to have "lashed out" and then hung up on Australian President Malcolm Turnbull over his insistence that the US stand by a refugee swap deal agreed with Barack Obama.

The President moved on to terrorism, amid continuing criticism over his Muslim ban.

(Image: REUTERS)

He said: "We have seen unimaginable violence in the name of religion. Acts of wanton slaughter against religious minorities.

"Horrors on a scale that defy description. Terrorism is a fundamental threat to religious freedom. It must be stopped and it will be stopped. It may not be pretty for a little while. It will be stopped."

He said Defence Secretary General James “Mad Dog” Mattis was “the real deal”.

He added: “You watch. You just watch. Things will be different.”

Trump went on: "We have seen threats of extermination against the Jewish people. We have seen a campaign of ISIS and genocide against Christians where they cut off heads - not since the middle ages have we seen that. We haven’t seen that. The cutting off of heads."

This is false.

Public beheading is the most common form of capital punishment in Saudi Arabia, where 347 executions took place between 2007 and 2010. The Kingdom of Saudi Arabia was performing executions for sorcery as recently as August 2014.

Saudi Arabia is not on the list of seven countries targeted by Trump’s travel ban.

(Image: REUTERS)

He said: “All nations have a duty to confront such violence and to confront it viciously if we have to. So I want to express clearly today to the American people, that my administration will do everything in its power to defend and protect religious liberty in our land. America must forever remain a tolerant society where all faiths are respected and where all of our citizens can feel safe and secure. We have to feel safe and secure.

“In recent days, we have begun to take necessary action to achieve that goal.

“Our nation has the most generous immigration system in the world.”

This is questionable.

While the US has the largest inflow of immigrants of any OECD country - with around a million immigrants entering the country each year - when it’s measured as a percentage of the population the US ranked 19th out of 24 countries in 2013.

But he said there were those that want to exploit America’s “generosity” to spread intolerance.

He said: “We will not allow a beachhead of intolerance to spread in our nation. You look all over the world and you see what’s happening. So in the coming days we will develop a system to ensure that those admitted into our country fully embrace our values of religious and personal liberty and that they reject any form of oppression or discrimination.

“We want people to come into our nation, but we want people to love us and to love our values. Not to hate us and to hate our values.

“We will be a safe country. We will be a free country and we will be a country where all our citizens can practice their beliefs without fear of hostility or fear of violence.”

The US already has one of the most stringent vetting regimes for refugees on the planet

(Image: AFP)

The process of applying for refugee status in the US is arduous and and can take up to 18 months to complete.

First they must register, be interviewed and granted refugee states by the United Nations.

Only the most vulnerable are granted refugee status and referred - less than 1 per cent of refugees world wide.

of refugees world wide. Once referred to the US, they face interviews with the State Department.

They undergo at least two background checks - but most refugees aged between 14 and 65 face three, including a higher level background check.

- but most refugees aged between 14 and 65 face three, including a higher level background check. Their fingerprints are screened against FBI and Homeland security databases to ensure they are not on watch lists.

to ensure they are not on watch lists. These are cross checked against fingerprints taken by the Defence Department from roadside bombs in Iraq.

Cases are then reviewed by the US immigration HQ - and further extensive, in-person interviews are conducted by the department of Homeland Security.

are conducted by the department of Homeland Security. They are screened for contagious diseases , go to cultural orientation classes and matched with a resettlement agency before facing another multi-agency security check. This is to catch any changes that might have taken place in the lengthy period between the first checks and leaving for the US.

, go to cultural orientation classes and matched with a resettlement agency before facing another multi-agency security check. This is to catch any changes that might have taken place in the When they arrive they face a final security check at an American airport.

So far the Trump administration has not outlined exactly how their ‘extreme vetting’ will be more extreme than the process already in place.

Writing for Politico, Mostafa Hassoun, a refugee in the US from Syria explained how intense the process is.

He wrote: "Over 15 months I was interviewed five times – in person, over the phone, by the United Nations and by the United States.

"They asked me about my family, my politics, my hobbies, my childhood, my opinions of the U.S., and even my love life.

"No less than four U.S. government agencies had the opportunity to screen me. By the time I received my offer to live in the United States, the U.S. officials in charge of my case file knew me better than my family and friends do."