"The President’s powers here are beyond question," Miller said in an interview on "Fox News Sunday."
He said that the federal appeals court that upheld a stay on the executive order "has a long history of being overturned and overreaching" and that the government is "pursuing every single possible action" to counter it.
"A district judge in Seattle cannot make immigration law for the United States, cannot give foreign nationals and foreign countries rights they do not have, and cannot prevent the President of the United States from suspending the admission of refugees from Syria," Miller said Sunday in an interview on NBC's "Meet the Press."
"What the judges did, both at the 9th and at the district level, was to take power for themselves that belonged squarely in the hands of the President of the United States," he said.
Miller said that there is "no such thing as judicial supremacy."
"We've heard a lot of talk about how all the branches of government are equal," Miller said. "That's the point. They are equal. There's no such thing as judicial supremacy."
Miller denied on "Fox News Sunday" that he and Trump's top strategist Steve Bannon played a major role in drafting the order.
"You and Steve Bannon were reportedly the prime movers behind the rollout of this executive order before it had been fully vetted," Fox News' Chris Wallace asked Miller. "Do you and Bannon take responsibility for all the problems with this rollout?"
"First of all, people are giving way too much credit to me and Steve Bannon," Miller replied. "Steve Bannon has no role whatsoever in drafting executive orders."