North Korean and American officials have since been unable to resume negotiations.

By launching short-range projectiles only, Mr. Kim appeared not to give up dialogue with the United States anytime soon, analysts said. Mr. Trump has repeatedly cited Mr. Kim’s moratorium on nuclear and long-range missile tests as a reason to continue diplomatic negotiations with North Korea.

Both Washington and the South also remain eager to keep North Korea on the diplomatic track.

They have been unusually reserved in their responses to North Korea’s weapons tests, calling the North’s new projectile a “guided weapon” even though the photos released in the official news media appeared to leave little doubt that it was a missile. Defense analysts in South Korea said the new projectile may have been based on the design of the Iskander, a solid-fuel short-range ballistic missile from the Russian military.

After the North Korean launches Saturday, Mr. Trump said that Mr. Kim “knows that I am with him & does not want to break his promise to me. Deal will happen!”

South Korea has yet to announce a plan to ship humanitarian aid to North Korea. But Mr. Moon is desperate to revive his role as a facilitator of dialogue between Washington and Pyongyang, the North’s capital, even if it entails providing humanitarian aid.

Both South Korea and the United States had used humanitarian aid shipments in the past as an incentive for North Korea to reduce tensions and return to dialogue. In recent years, American officials have been increasingly skeptical about the approach, arguing that the North should have bought food for its own people with the money it spent on building nuclear weapons. Nor did humanitarian aid help persuade North Korea to give up its nuclear weapons development, they said.

But Mr. Trump has recently hinted at flexibility.

When Mr. Moon met him at the White House on April 11, Mr. Trump said he and the South Korean leader were discussing humanitarian aid for the North.

“I’m O.K. with that, to be honest,” he told reporters at the time. “South Korea is doing certain things to help out with food and various other things for North Korea.”

United Nations sanctions against North Korea do not ban humanitarian aid for the country. But after North Korea launched a ballistic missile over Japan in 2017, South Korea was forced to shelve its plan to donate $8 million to the World Food Program and United Nations Children’s Fund to help North Korea’s malnourished children and pregnant women.