WASHINGTON — Vice President Mike Pence on Sunday defended President Trump’s personal attack on the federal judge who blocked his travel ban on seven predominately Muslim countries, saying that the president’s remarks did not risk undermining the bedrock principle of the separation of powers.

Asked about Mr. Trump’s reference on Twitter to the “so-called judge” who ordered a stay of the president’s executive order, Mr. Pence said on NBC’s “Meet the Press”: “Well, look, the president of the United States has every right to criticize the other two branches of government. And we have a long tradition of that in this country.”

“The judge’s actions in this case,” Mr. Pence added, “making decisions about American foreign policy and national security, it’s just very frustrating to the president, to our whole administration, to millions of Americans who want to see judges that will uphold the law and recognize the authority the president of the United States has under the Constitution to manage who comes into this country.”

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After nearly 20 hours of silence on Twitter, Mr. Trump returned on Sunday afternoon, accusing the judge of imperiling the country.

But some Republicans said Mr. Trump’s attacks were inappropriate. The Senate’s top Republican, Mitch McConnell of Kentucky, said on CNN’s “State of the Union” that it was “best not to single out judges.”

“We all get disappointed from time to time,” Mr. McConnell said. “I think it is best to avoid criticizing them individually.”

It is the role of the courts, he said, to decide “whether or not the executive order of the president that is issued is valid.” He said Congress was unlikely to act on the matter.

The comments came hours after the United States Court of Appeals for the Ninth Circuit, in San Francisco, rejected an initial Justice Department request to block the stay that was issued on Friday by Judge James Robart of United States District Court for the Western District of Washington.

Speaking on “Fox News Sunday,” Mr. Pence said the administration would continue to “use all legal means at our disposal to stay that order.” He framed the issue as a matter of national security.

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“There’s simply no question under the Constitution, and frankly under federal law, that the president of the United States has the authority in the interest of national security to determine who has the right to come into this country,” Mr. Pence said on “This Week.”

Mr. Pence’s language was markedly less personal than that of Mr. Trump, who has repeatedly attacked the ruling on Twitter, singling out Judge Robart and asking “What is our country coming to” when a court can halt an order that affects the nation’s security.

Critics in both parties said the president had demonstrated a lack of understanding of or a disregard for the nation’s three equal branches of government.

“I’ll be honest, I don’t understand language like that,” Senator Ben Sasse, Republican of Nebraska, said on “This Week.” “We don’t have so-called judges. We don’t have so-called senators. We don’t have so-called presidents.”

“We have people from three different branches of government who take an oath to uphold and defend the Constitution,” Mr. Sasse said.

Democrats were less restrained and said the issue would color the battle over the nomination of Judge Neil M. Gorsuch, Mr. Trump’s choice for the Supreme Court.

“When he attacks the independence of the judiciary, I think it does focus on the fight before us now,” Senator Amy Klobuchar, Democrat of Minnesota, said on “This Week.” “And that is that we want to see a nominee that is independent, not just of a president, but is not making decisions based on ideology but instead making decisions based on precedent.”

Ms. Klobuchar said the attack on Judge Robart fit a pattern for Mr. Trump.

“He attacked Judge Curiel during the course of his campaign on the Trump University case. He attacked the acting attorney general,” she said, referring to Judge Gonzalo P. Curiel, whom Mr. Trump accused of having a conflict of interest because of his Mexican heritage, and Sally Q. Yates, whom Mr. Trump fired after she ordered the Justice Department not to defend the executive order.

Senator Dianne Feinstein of California, the top-ranking Democrat on the Judiciary Committee, predicted that the matter would ultimately be decided by the Supreme Court.

“The president is not a dictator,” Ms. Feinstein said on “Fox News Sunday.” “The framers of our Constitution wanted a strong Congress for the very reason that most of these kinds of things should be done within the scope of lawmaking. This is done within the scope of executive power.”