Campaigners opposed to Donald Trump's travel ban are celebrating after the White House said it would not challenge an appeals court ruling in the Supreme Court.

The President had said he was confident that his lawyers would win the argument before the country’s highest court – saying on twitter 'see you in court'. But against the risk that he could suffer his fourth legal setback over the ban on travel to the US for people from seven Muslim-majority countries, the White House announced it would not for now pursue the legal battle any further.

It came as Mr Trump said he would likely introduce another, or reworked executive order, to address the issue of immigration to the US from certain countries.

Speaking to reporters on Air Force One on his way to Florida, he said he was confident that he could win any legal battles. But he indicated he was also thinking about alternative strategies.

“We also have a lot of other options, including just filing a brand new order,” he said, according to the Associated Press.

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“We need speed for reasons of security. So it could very well be that we do that.”

He said that could happen as early as Monday or Tuesday of next week. “I'd like to surprise you,” he said.

Asked as to what a new order may contain, he said: "New security measures. We have very, very strong vetting. I call it extreme vetting and we're going very strong on security. We're going to have people coming to our country that want to be here for good reasons."

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A day after a federal appeals court rejected his executive order to ban travel from seven majority-Muslim countries, Mr Trump said on Friday he would introduce “something new” to replace the controversial order.

Mr Trump suffered the embarrassing defeat after the 9th Circuit Court of Appeals' unanimous decision to pause the president's executive order. In response to his second federal court loss in less than a week, Mr Trump furiously told the court he would “SEE YOU IN COURT,” via Twitter.

During a joint press conference with Japanese Prime Minister Shinzo Abe, Mr Trump said he would announce new security measures as soon as next week. It remains unclear if the new measures would be separate from the controversial executive order that currently hangs in limbo, or a reworking of it.

“Safety is one of the reasons I’m standing here today, the security of our country,” Mr Trump said.

“So, we'll be doing something very rapidly having to do with additional security for our country. You’ll be seeing that sometime next week.”