The San Francisco federal appeals court on Thursday unanimously refused to reinstate President Donald Trump's ban on refugees and nationals from seven Muslim-majority countries, dealing his controversial law-and-order agenda a major blow.

The San Francisco federal appeals court's ruling on Trump's executive order - issued on Jan 27 with no prior warning and suspended by a lower court a week later - capped a turbulent first three weeks of his presidency.

A defiant Trump quickly pledged to battle on, tweeting within minutes of the decision: "See you in court, the security of our nation is at stake!"