"A clear victory for our national security," Trump declared in a statement. But it was a victory for common sense too, with the court ruling that a significant but unspecified number of people who would have been barred should still be allowed to enter the US.

"As President, I cannot allow people into our country who want to do us harm," Trump said. "I want people who can love the United States and all of its citizens, and who will be hardworking and productive."

But rejecting the blanket nature of the ban, the justices declared that those with good reason to enter the US could continue to do so. They include those with family or relationship connections with people already in the US and others with legitimate business or educational engagements.

Referring to the circumstance of some among the tens of thousands who had visas revoked when Trump first sprung his executive order on America and the world, the court's unsigned opinion said: "The facts of these cases illustrate the sort of relationship that qualifies. For individuals, a close familial relationship is required.

"A foreign national who wishes to enter the [US] to live with or visit a family member … clearly has such a relationship. As for entities, the relationship must be formal, documented, and formed in the ordinary course, rather than for the purpose of evading [the executive order]."

And the court will still rule, in October, on charges that Trump was in breach of the constitution in his March revision of the ban, which had its genesis in his calls during the 2016 election campaign for a temporary ban on all Muslims entering the US. That ban was to be for 90 days in the case of ordinary travellers and 120 days for refugees, during which the administration was to review its screening and vetting of visa applicants.

On gaining office, Trump asked former New York mayor Rudy Giuliani to help devise his "Muslim ban" – but asked that it be done the "right way legally". And in celebrating Monday's decision, Trump had forgotten a recent tweet in which he made clear that remained his preference: "The Justice Dept should have stayed with the original Travel Ban, not the watered down, politically correct version they submitted to S.C."

Iraq was dropped from the first list amid legal protests and chaos as travellers were detained on arrival at American airports and deported, or were barred from boarding their flights to the US. Iraq's exclusion was apparently at the behest of Defence Secretary James Mattis, who saw Iraq's inclusion on the list as an impediment to cooperation between Washington and Baghdad in the war against Islamic State.

The court's "good reason" test for entry to the country likely means there will not be a repeat of the mass protests, emotional outpourings and the caravans of lawyers setting up in airport terminals sparked by Trump's first draft.

The administration recently predicted that if cleared, the ban would be operational within 72 hours of the court's ruling.

Four justices, including Trump appointee Justice Neil Gorsuch, dissented, arguing that the revised ban, as written by the administration, should have been reinstated. Warning of a likely flood of legal challenges, Justice Clarence Thomas wrote for the dissenters: "I fear that the court's remedy will prove unworkable.

"Today's compromise will burden executive officials with the task of deciding - on peril of contempt - whether individuals from the six affected nations who wish to enter the United States have a sufficient connection to a person or entity in this country."

Monday's ruling was an interim response to a White House application that lower appeal court rulings against the ban should be set aside as the cases made their way through the legal system. Several lower courts had objected to the ban, invoking the First Amendment's ban on government establishment of religion and in one case, the language of Trump's campaign rhetoric, which was read as proof that the ban "drips with religious intolerance, animus and discrimination."

And given the timeline, the proposed 90 and 120-day terms of the ban will have expired before the case is argued before the Supreme Court, the justices seemed to be saying that the business of the ban might be moot by the time the case is argued in October.

For the record, in the 150-odd days since Trump signed his first executive order to impose the travel ban, there have been no recorded terror attacks by immigrants or refugees in the US.