US President Donald Trump has taken to Twitter again to slam the federal judge who blocked a travel ban on citizens of seven mainly Muslim nations.

As the first major legal battle of the Trump administration intensifies, Mr Trump further criticised the role of the courts and defended the travel ban, citing the risks of Judge James L Robarts' ruling on national security.

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His Vice-President, Mike Pence, also stepped up to defend the Trump administration's actions, saying Mr Trump had every right to criticise the judge.

Mr Trump earlier blasted Judge Robart as a "so-called judge", a day after the Seattle jurist issued a temporary restraining order on the ban.

A US appeals court later on Saturday denied the Government's request for an immediate stay of the ruling.

"The President of the United States has every right to criticise the other two branches of government," Mr Pence told NBC's Meet the Press.

It is unusual for a sitting president to attack a member of the judiciary, which the US constitution designates as a check on the power of the executive branch and congress.

US senator Patrick Leahy, the ranking Democrat on the Senate Judiciary Committee, said Mr Trump seemed intent on precipitating a constitutional crisis.

Some Republicans also expressed discomfort with the situation.

"I think it is best not to single out judges for criticism," Senate majority leader Mitch McConnell told CNN.

"We all get disappointed from time to time at the outcome in courts on things that we care about. But I think it is best to avoid criticising judges individually."

Republican senator Ben Sasse, a vocal critic of Mr Trump, was less restrained:

"We don't have so-called judges … we don't have so-called presidents, we have people from three different branches of government who take an oath to uphold and defend the constitution," he told ABC America.

The ruling by Judge Robart, along with the decision by the 9th US Circuit Court of Appeals in San Francisco to deny the Government's request for an immediate stay, dealt a blow to Mr Trump barely two weeks into his presidency.

It could also be the precursor to months of legal challenges to Mr Trump's push to clamp down on immigration, including through the construction of a wall on the US-Mexican border.

Mr Trump, who during his presidential campaign called for a temporary ban on Muslims entering the United States, has vowed to reinstate the travel ban on citizens from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen and a 120-day bar on all refugees.

He says the measures are needed to protect the United States from Islamist militants. Critics say they are unjustified and discriminatory.

A woman participates in a rally in support of President Donald Trump outside Trump Tower. ( Reuters: Andrew Kelly )

How did we get here?

The legal limbo will prevail at least until the 9th US Circuit Court of Appeals rules on the Government's application for a stay of Judge Robart's ruling.

The court was awaiting further submissions from the states of Washington and Minnesota on Sunday, and from the Government within the next 24 hours. The final filing is due on Monday (12:00pm Tuesday AEDT).

The uncertainty has created what may be a short-lived opportunity for travellers from the seven affected countries to get into the United States.

Reacting to the latest court ruling, Iraqi Government spokesman Saad al-Hadithi said: "It is a move in the right direction to solve the problems that it caused."

Mr Trump's January 27 travel restrictions have drawn protests in the United States, provoked criticism from US allies and created chaos for thousands of people who have, in some cases, spent years seeking asylum.

In his ruling on Friday, Judge Robart questioned the use of the September 11, 2001 attacks on the United States as a justification for the ban, saying no attacks had been carried out on US soil by individuals from the seven affected countries since then.

For Mr Trump's order to be constitutional, Judge Robart said, it had to be "based in fact, as opposed to fiction".

The 9/11 attacks were carried out by hijackers from Saudi Arabia, the United Arab Emirates, Egypt and Lebanon, whose nationals were not affected by the order.

In a series of tweets on Saturday, Mr Trump attacked "the opinion of this so-called judge" as ridiculous.

"What is our country coming to when a judge can halt a Homeland Security travel ban and anyone, even with bad intentions, can come into US?" he asked.

Mr Trump told reporters at his private Mar-a-Lago resort in Florida:

"We'll win. For the safety of the country we'll win."

The Justice Department appeal criticised Judge Robart's legal reasoning, saying it violated the separation of powers and stepped on the President's authority as commander-in-chief.

The appeal said the state of Washington lacked standing to challenge the order and denied that the order "favours Christians at the expense of Muslims".