Stephen Miller told US media the court ruling was a “judicial usurpation of power”, and that “the president’s powers here are beyond question”.
Trump’s attempt to reinstate his ban – which had banned people with visas from seven largely Muslim countries from travelling to the US - was rejected by the court on Thursday.
A federal judge has issued a nationwide block on the travel ban.
Trump has said he may still fight the case in the courts, or issue a new executive order.
In an interview with Fox News on Sunday, Miller accused the 9th US Circuit Court of Appeals, which upheld the block on Trump’s order, of “overreaching”.
He also told media: “We have equal branches of government in this country. The judiciary is not supreme."
Under the US system courts can declare laws or acts by the president as unconstitutional.
White House adviser attacks court over Trump's travel ban
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