The appeal aimed to reverse a federal judge's Friday order that lifted the travel ban, warning the decision posed an immediate harm to the public.
“Appellants’ request for an immediate administrative stay pending full consideration of the emergency motion for a stay pending appeal is denied,” the late-night order appeals court order stated.
It said a reply from the Department in support of the emergency appeal was due on Monday.
The state department said last week that up to 60,000 people had their visas revoked as a result of Trump's ban, although a justice department lawyer put the number at closer to 100,000.
The restrictions on all refugees and travellers from the seven countries went into effect a week ago, wreaking havoc at airports across the US and leaving travellers trying to reach the country in limbo.
The political backlash for Trump has been equally severe, with the order driving numerous mass protests.