Officials in Washington have expressed concern about the growing rupture between Japan and South Korea, worried that the end of the intelligence-sharing deal would send the wrong signal to China and North Korea, which have long sought to undermine American influence in the region.

Without the agreement, Tokyo and Seoul will have to exchange sensitive military intelligence through Washington, which has separate intelligence-sharing deals with both nations. But such an arrangement could slow down the information-sharing at critical moments, like immediately after a North Korean missile launch, analysts said.

When North Korea’s recent series of launches began in late July — involving what South Korean officials characterize as two new types of short-range ballistic missile, as well as a new guided multiple-tube rocker launcher — it blamed South Korea and the United States, for carrying out joint military exercises to which the North strongly objects.

President Trump has shrugged off the recent launches, calling them “smaller ones.”

Speaking to reporters on Friday night as he was leaving the White House for the Group of 7 meeting of industrialized nations, Mr. Trump said the tests did nothing to complicate his relationship with North Korea’s leader, Kim Jong-un, or his hopes for denuclearization talks.

“He likes testing missiles,” Mr. Trump said. “But we never restricted short-range missiles. Many nations test those missiles.”

The president said that the United States had recently “tested a very big one.”

Earlier this month, he said Mr. Kim had sent him a letter that included a “small apology” for the tests, and which said that the North wanted to begin a dialogue with Washington as soon as the joint military drills were over.

The drill ended on Tuesday, but North Korea has continued to express displeasure toward the United States. On Friday, its foreign minister, Ri Yong-ho, called Secretary of State Mike Pompeo a “die-hard toxin of the U.S. diplomacy,” according to a statement carried by the North’s official Korean Central News Agency.