Donald Trump has signed a new executive order that restricts travel to the US for people from six Muslim majority countries - a slightly watered-down version of his previous order but one that campaigners said still “heartlessly targets" the world's most vulnerable people.

The new directive aims to address legal issues with the original order, which caused confusion at airports, sparked protests around the country and was ultimately blocked by federal courts.

In stark contrast to the chaotic, almost shambolic manner in which the president's first order was rolled out in January, this new, amended measure was accompanied by a sober televised appearance by three of his most senior officials.

Written with the experience of having seen his first order stayed by several federal causes, this revised order is said to be narrower and specifies that a 90-day ban on people from Sudan, Syria, Iran, Libya, Somalia and Yemen does not apply to those who already have valid visas.

The White House also dropped Iraq from the list of banned countries. This was done amid pressure from the Pentagon, which was furious that it undermined relations with a country with which the US is currently engaged in the fight against Isis. Furthermore, a number of Iraqis who had worked for the US military in roles such as translators had found themselves caught up in the ban and detained at US airports.

Mr Trump privately signed the new order on Monday morning, while Homeland Security Secretary John Kelly, Secretary of State Rex Tillerson and Attorney General Jeff Sessions formally unveiled the new edict.

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The low-key approach was a contrast to the first version of the order, signed in a high-profile ceremony at the Pentagon's Hall of Heroes as Secretary of Defence James Mattis stood by the president's side.

"This revised order will bolster the security of the United States and her allies," said Mr Tillerson.

Refugee and immigration rights officials, said the initiative by Mr Trump will further the misery confronting the world’s refugees.

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David Miliband, head of the International Rescue Committee, which provides humanitarian aid in 40 countries and resettles security-vetted refugees to 28 US cities, said the order “heartlessly targets the most vetted and most vulnerable population to enter the United States”.

He added: “This ban doesn’t target those who are the greatest security risk, but those least able to advocate for themselves. Instead of making us safer, it serves as a gift for extremists who seek to undermine America.”

More than two dozen lawsuits were filed in US courts against the original travel ban and the state of Washington succeeded in having it suspended by the 9th Circuit court of Appeals by arguing that it violated constitutional protections against religious discrimination.