Donald Trump no longer supports a total ban on Muslims entering the United States, his running mate said on Thursday.

Vice-presidential candidate Mike Pence, currently governor of Indiana, signalled a shift from one of Trump's most provocative proposals during a round of television interviews.

The Republican presidential candidate first called last December for a "total and complete shutdown of Muslims entering the United States" following an Islamic State-inspired mass shooting in San Bernardino, California, in which 14 people were killed.

Trump's pledge to ban Muslim immigrants to the US has been branded discriminatory and probably a violation of the US Constitution's guarantee of freedom of religion.

Democrats have used Trump's policy to declare him a bigot.

In recent months, Trump has said he would suspend immigration from countries where Islamist militants are active but has left vague as to whether this amounted to a narrowing or an expansion of his original policy position.

Pence said on Thursday that if elected on November 8, Trump would suspend immigration from "countries that have been compromised by terrorism."

Asked if this amounted to a ban on Muslims, Pence said on MSNBC's 'Morning Joe' show: "Of course not."

On CNN's 'New Day,' Pence was asked why, given that he had been against the ban before becoming Trump's running mate, he was not opposing it now.

"Well, because it's not Donald Trump's position now," replied Pence.

Analysts have noted that Trump's original December 7 statement in which he set out the ban is still on his campaign website.

Additional reporting by Reuters