"We assess those factors in light of the limited evidence put forward by both parties at this very preliminary stage and are mindful that our analysis of the hardships and public interest in this case involves particularly sensitive and weighty concerns on both sides.
"Nevertheless, 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, and we therefore deny its emergency motion for a stay."
This means the travel ban is still in limbo. The government will now likely take its appeal to the Supreme Court, where the ban's legality will be decided.
Mr Trump took to Twitter to make his thoughts on the ruling known.
"It's a political decision, we're going to see them in court, and I look forward to doing that," Mr Trump told reporters in the White House. "It's a decision that we'll win, in my opinion, very easily."
The court rejected the administration's claim that it did not have the authority to review the president's executive order.
"There is no precedent to support this claimed unreviewability, which runs contrary to the fundamental structure of our constitutional democracy," the court said.
"Rather than present evidence to explain the need for the executive order, the government has taken the position that we must not review its decision at all. We disagree, as explained above."
Mr Trump's executive order temporarily suspended America's refugee program and immigration from seven majority-Muslim countries that have raised terrorism concerns, including Iraq, Iran, Sudan, Libya, Somalia, Yemen and Syria.
His decree slapped a blanket ban on nationals for 90 days and barred all refugees for 120 days.
Refugees from Syria were blocked indefinitely.
US District Judge James Robart in Seattle issued a temporary order halting the ban last week after two states, Washington and Minnesota, sued.
Justice Department lawyers appealed to the 9th Circuit, arguing that the president has the constitutional power to restrict entry to the United States and that the courts cannot second-guess his determination that such a step was needed to prevent terrorism.
Each side had half an hour to defend their positions, with the judges asking tough questions throughout.
During the hearing the judges expressed scepticism over the need for the travel ban that covers seven predominantly Muslim countries, but also downplayed the importance of public comments that suggested the ban targeted Muslims.
