The Trump administration will threaten to impose sanctions on the International Criminal Court if it pursues an investigation of American troops in Afghanistan, opening a harsh new attack on an old nemesis of many on the political right.

“The United States will use any means necessary to protect our citizens and those of our allies from unjust prosecution by this illegitimate court,” according to the text of a speech President Trump’s national security adviser, John R. Bolton, plans to deliver on Monday.

“We will ban its judges and prosecutors from entering the U.S.,” Mr. Bolton will say. “We will sanction their funds in the U.S. financial system, and, we will prosecute them in the U.S. criminal system. We will do the same for any company or state that assists in an I.C.C. investigation of Americans.”

Mr. Bolton will also announce that the United States will shut down the Palestine Liberation Organization’s office in Washington — a decision linked to the International Criminal Court, which he will say is being prodded by the Palestinians to investigate Israel. The State Department confirmed the shutdown plan Monday.