JERUSALEM — President Trump’s national security adviser, John R. Bolton, warned Tehran on Sunday not to “mistake U.S. prudence and discretion for weakness,” saying that military action against Iran remained very much an option even though the United States last week called off one military strike.

Tensions between the two countries had brought Mr. Trump to the brink of ordering a retaliatory strike over explosions on oil tankers in the Gulf of Oman and the Iranian downing of an American surveillance drone.

The United States said there was no doubt that Iran was responsible for the attacks on the vessels near the Strait of Hormuz, but Iran has denied it. Tehran has also said that the drone breached its air space, though American officials said the drone had been over international waters.

“No one has granted them a hunting license in the Middle East,” Mr. Bolton said on Sunday at an appearance in Jerusalem alongside Prime Minister Benjamin Netanyahu of Israel.