“I call on leaders in both parties in Washington to strongly condemn these actions in no uncertain terms,” Governor Hogan, a Republican, said. “It is vital to our constitutional system that the justices be able to carry out their duties without fear of violence against them and their families.”

At a news conference on Wednesday to discuss the school shooting in Uvalde, Mr. Garland said that the threat against Justice Kavanaugh was “behavior that we will not tolerate.” He added that last month he “accelerated the protection of all the justices’ residences 24/7,” and that he had met with the Supreme Court marshal, the F.B.I., the U.S. Marshals and his own prosecutors to “ensure every degree of protection available is possible.”

“Threats of violence, and actual violence, against the justices, of course, strike at the heart of our democracy,” Mr. Garland said. “We will do everything we can to prevent them, and to hold people who do them accountable.”

Speaking to reporters aboard Air Force One on Wednesday, Karine Jean-Pierre, the White House press secretary, said that President Biden “condemns the actions of this individual in the strongest terms and is grateful to law enforcement for quickly taking him into custody.”

“As the president has consistently made clear, public officials, including judges, must be able to do their jobs without concern for their personal safety or that of their families,” Ms. Jean-Pierre said. “Any violence threats — threats of violence or attempts to intimidate justices — have no place in our society. He has said that himself, and we have been forceful from the podium many times.”

In a bulletin issued on Tuesday, the Department of Homeland Security said that after the publication of the leaked draft opinion in the abortion case, advocates for and against abortion rights have “encouraged violence” on public forums, “including against government, religious, and reproductive healthcare personnel and facilities, as well as those with opposing ideologies.”