Three weeks in office, the Trump administration is still trying to find its footing on foreign policy, especially in areas like North Korea that have not been Mr. Trump’s main focus. Secretary of State Rex W. Tillerson was sworn in on Feb. 1 and does not even have a deputy, much less a full team of trusted advisers, in place.

That North Korea’s latest test came while Mr. Trump was hosting Mr. Abe for a multiday set of meetings, meals and golfing, first at the White House and then at Mr. Trump’s Mar-a-Lago estate in Palm Beach, Fla., was seen as no accident. And it may be that Mr. Abe counseled Mr. Trump on his response. In his own comments while he stood beside Mr. Trump, Mr. Abe called the launch “absolutely intolerable.”

Asia experts and members of Congress praised Mr. Trump for reaffirming American support for Japan but lamented that he did not mention South Korea at the same time. “I was glad he issued the statement with the prime minister of Japan, but he ought to do it quickly with South Korea,” Senator Chuck Schumer of New York, the Democratic minority leader, said on “Face the Nation” on CBS. “South Korea is probably more susceptible to North Korea’s virulence than any other country.”

White House officials on Sunday remained quiet about the test and their emerging strategy. Stephen Miller, the president’s senior adviser for policy, said Mr. Trump had sent a strong signal with his joint appearance with Mr. Abe.

“But we’re going to be sending another signal very soon, and that signal is when we begin a great rebuilding of the armed forces of the United States,” he said, also on “Face the Nation.” “President Trump is going to go to Congress and ask them to invest in our military so once again we will have unquestioned military strength beyond anything anybody can imagine.”

Short of military action, the menu of options available for Mr. Trump is not significantly better than it was for his predecessors. The United States and the United Nations have already imposed an array of wrenching sanctions and have largely isolated North Korea from much of the world.

On his first overseas trip since taking office, Defense Secretary Jim Mattis visited Japan and South Korea to reassure them of America’s support despite statements by Mr. Trump during the campaign that called it into question. South Korean officials agreed to press ahead with development of a new missile defense system called Terminal High-Altitude Area Defense, or Thaad.