The unanimous ruling, by a panel of three judges in San Francisco, will likely pave the way for a showdown in the Supreme Court.
However, the appeals court justices expressed doubt that Mr Trump’s government would be successful if it launched another appeal.
In off-camera remarks to reporters at the White House, the President insisted he was confident that his administration would eventually win the case “very easily”.
Mr Trump branded the decision as “political” – and moments after the ruling, he tweeted: “SEE YOU IN COURT, THE SECURITY OF OUR NATION IS AT STAKE!”
Washington Governor Jay Inslee, who represents one of the states which took on the government, replied: “Mr President, we just saw you in court, and we beat you.”
The US Justice Department was more measured in its response than Mr Trump – and a spokeswoman said it was “considering its options”.
In their judgment, the appeals court said the US Justice Department had not offered “any evidence” of national security concerns which had justified banning migrants, visitors and refugees from seven Muslim-majority countries.
The judges concluded that the government had provided no evidence that any citizen from Iraq, Iran, Libya, Somalia, Sudan, Yemen and Syria had perpetrated an attack on American soil.
In addition, no evidence was offered which explained the urgent need for his executive order to take effect immediately.
Lawyers from Washington state and Minnesota – which mounted the legal challenge against Mr Trump – had offered compelling evidence that even a temporary reinstatement of the travel ban would cause harm, and raised serious allegations of religious discrimination.
The ruling means migrants, visitors and refugees from the affected countries can continue to travel to the US if they have valid visas or green cards – something which Mr Trump had attempted to stop with his executive order.
SEE YOU IN COURT, THE SECURITY OF OUR NATION IS AT STAKE!
In its arguments, the Justice Department had insisted that the President had the constitutional power to restrict entry to the US – and that the courts should not attempt to second-guess his determination that such measures were needed to prevent acts of domestic terrorism.
The judges said: “On the one hand, the public has a powerful interest in national security and in the ability of an elected president to enact policies. 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.”
Mr Trump’s executive order had been temporarily suspended nationwide by Judge James Robart in Seattle last week.
Following that ruling, the President branded Mr Robart’s ruling as “ridiculous” – and described him as a “so-called judge”.
Sky’s US Correspondent Hannah Thomas-Peter said: “As Donald Trump’s tweet indicates, he is likely to be utterly furious about this ruling.
“It will embarrass a man who ran on a promise to act quickly and decisively on matters of ‘national security’.
“It will sting even more that he has been thwarted by his country’s court system – full of the kind of grey-haired establishment figures he railed against during his insurgent campaign.
“Donald Trump is at his most unpredictable when angry or backed in to a corner – and now, he is both these things.”