“I do not see any need to increase the number of forces we have in the Middle East at this time,” Mr. Mattis said, speaking in Tokyo at a news conference as he wound up his visits to Japan and South Korea, his first foreign trip as defense secretary.

Michael T. Flynn, President Trump’s national security adviser, said this week that the United States was putting Iran “on notice” because of its recent missile test and support for Houthi rebels in Yemen, whom the United States has accused of threatening American vessels in the Red Sea and attacking a Saudi Navy patrol boat.

The Trump administration imposed economic sanctions on Friday against 25 Iranians and companies that it said were connected with Iran’s missile program and the country’s Islamic Revolutionary Guard Corps. But so far, the White House has not announced military steps to strengthen its presence in the region. No American aircraft carrier is currently deployed in the Persian Gulf, though the Navy was expected to rotate one into the area.

Mr. Mattis defended the decision to put a spotlight on Iran’s behavior, saying that it was important to make Iran recognize that “it is getting the attention of a lot of people.”