Three judges from the 9th US Circuit Court of Appeals declined to block a ruling by a lower court ruling that suspended the ban.
The new rules - enshrined in a January 27 executive order by US President Donald Trump - had previously barred travelers from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen entering the US.
An appeal to the US Supreme Court is possible, with Trump tweeting swiftly - and in capital letters - after Thursday's ruling that the legal battle over the ban is not over.
The government had made a request to reinstate the measure on an emergency basis, which the judges considered to be unwarranted.
"We hold that the government has not shown a likelihood of success on the merits of its appeal, nor has it shown that failure to enter a stay would cause irreparable injury," the court wrote in its decision.
The San Francisco court decision was not about the ban itself, but about whether it should be allowed to go into effect immediately. The three judges rejected in strong terms the Justice Department's argument that the president alone had discretion over immigration policy, without room for review by the courts.
"There is no precedent to support this claimed unreviewability, which runs contrary to the fundamental structure of our constitutional democracy," the decision read.
Some legal experts have interpreted the language of the ruling to indicate that a suit claiming the ban itself is unconstitutional would have a good chance of suceeding. The states of Washington and Minnesota have brought a case arguing the government's ban violates the constitution. The ruling on that suit is still pending.
Two sides to weigh
Federal appeals court judges said they weighed compelling arguments about the public interest on both sides when determining whether to uphold the suspension of the travel ban.
"On the one hand, the public has a powerful interest in national security and in the ability of an elected president to enact policies," the court said. "And on the other, the public also has an interest in free flow of travel, in avoiding separation of families, and in freedom from discrimination."
The judges, who heard evidence in the case on Tuesday, said there was no evidence presented by the government that anyone from those countries had perpetrated a terrorist attack in the US.
The Justice Department, whose job it is to put the executive's case, said it was reviewing the decision and weighing its options. The man who will lead Trump's fight at the helm of the department, Jeff Sessions, was sworn in as US attorney general on Thursday.
A temporary restraining order halting the ban was issued last week by US District Judge James Robart in Seattle, after Washington state and Minnesota challenged the order.
Unconstitutional religious block?
Government lawyers said the ban was a "lawful exercise" of presidential authority, adding that the seven countries had raised terrorism concerns. However, the states claimed the order was unconstitutional, blocking entry on the basis of religion.
Limiting entry to the United States was a central premise of Trump's 2016 presidential campaign. He originally proposed as a temporary ban on all Muslims, and has voiced frustration at the legal challenge to his order.
rc/gsw (AP, Reuters)