Donald Trump's campaign has denied reports that he is backtracking on his plan to ban all Muslims from entering the US.

CNN reported that Trump was softening his plan for "a total and complete shutdown on Muslims entering the United States".

"His campaign is putting the finishing touches on a policy memo that would change his proposed ban on Muslim immigration to the United States. Instead of focusing the ban on Muslims, Trump would ban immigrants coming from countries with known terrorism links, training and equipment," CNN reported.

A spokesperson for Trump's campaign responded: "This is not accurate. There has been no change from the exchanges over the weekend."

However, Trump's language surrounding immigration has shifted in recent weeks.

When first announced in December, Trump's proposal stated that there would be "a total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what is going on."

That the ban would be imposed on Muslims from both Muslim-majority countries and others was at the time reiterated by Trump's senior policy advisor Sam Clovis.

But during his recent visit to Scotland, Trump reportedly said it wouldn't bother him if Scottish Muslims came to the US. Similarly, in a speech following the Orlando shooting, he said: "When I am elected, I will suspend immigration from areas of the world when there is a proven history of terrorism against the United States, Europe or our allies, until we understand how to end these threats."

When the CNN report first came out, Trump's spokesperson Katrina Pierson did not deny the allegations.

"It's only really a change if you never knew what the ban was to begin with," she said.

"If you are coming into this country and you cannot be vetted, then you should not be allowed in until you can be vetted. This is not rocket science."