SEOUL, South Korea — South Korea on Friday adamantly rejected an American request to continue sharing military intelligence with Japan, as the two American allies remained locked in festering disputes over trade and history.

Mark T. Esper, the United States secretary of defense, visited Seoul to attend an annual defense meeting and personally implore his South Korean counterpart to remain in the intelligence-sharing pact with Japan, known as the General Security of Military Information Agreement, or GSOMIA.

Washington considers the agreement important for the security and stability of the region. South Korea and Japan face similar threats from North Korea and China, but there is a deep-seated mistrust rooted in Japan’s colonial rule of Korea from 1910 to 1945.

“The only ones who benefit from the expiration of GSOMIA and continued friction between Seoul and Tokyo are Pyongyang and Beijing,” Mr. Esper said during a joint news conference with his counterpart, Jeong Kyeong-doo, on Friday.

“That reason alone should be powerful enough for all of us to sit down and make sure that we restore our alliance and partnership where it was,” Mr. Esper added.

Mr. Jeong said South Korea would abandon the agreement next Friday unless Japan removed the export restrictions it had earlier imposed against South Korea.

That sentiment was echoed by the office of President Moon Jae-in. “Our decision to terminate GSOMIA was inevitable,” Ko Min-jung, a spokeswoman for Mr. Moon, said in a radio interview earlier on Friday. “If we revoke our decision unilaterally without any change in Japan’s exports restrictions and in relations between South Korea and Japan, it would only prove that we made our original decision not prudently enough. That was not the case.”

When South Korea announced in August that it would abandon the agreement, despite repeated objections from Washington, it created a rare fracture in the alliance between South Korea and the United States. Washington issued several statements expressing strong disappointment with its allies in Seoul.

The agreement took effect in 2016 and had become a symbol of Washington’s successful efforts to persuade its two key East Asian allies to set aside their mutual enmity in order to counter China’s growing military influence and the nuclear and missile threat from North Korea.

Although South Korea insists that its commitment to the alliance with Washington remains intact, its decision to quit GSOMIA showed how easily such efforts by the United States can be trumped by recurring historical disputes between South Korea and Japan.

Simmering tensions between the two neighbors exploded after South Korea’s Supreme Court ruled late last year that Japanese companies should pay reparations to South Koreans for forced labor during the colonial era. Japan insists that all wartime claims were settled when it and South Korea established diplomatic ties in 1965.

Japan later imposed a series of restrictions on security-related products exported to South Korea. In August, South Korea retaliated by announcing an end to GSOMIA. Although Mr. Moon and Prime Minister Shinzo Abe of Japan met briefly in Bangkok last week, their governments have yet to narrow their differences.

During his trip to Seoul, Mr. Esper also discussed how to bring North Korea back to denuclearization talks and mounting friction between South Korea and the United States over how to share the cost of keeping 28,500 American troops in South Korea.

The issue of cost has become particularly contentious under President Trump, who has insisted that South Korea and other allies shoulder the expense of maintaining American bases on their soil.

In February, South Korea agreed to contribute about 1.04 trillion won, or $925 million, this year, an 8.2 percent increase from last year. Washington is now demanding that South Korea contribute as much as $4.7 billion next year, according to South Korean news media and lawmakers.

On Friday, Mr. Esper would not name an exact figure but said South Korea is a “wealthy country” that “could and should” pay more. Mr. Jeong said the United States and South Korean negotiators were trying to work out a “fair and reasonable” deal. Mr. Trump has often questioned the cost of stationing American troops abroad.

The two allies are also still working to bring North Korea back to the table to discuss abandoning its nuclear weapons and missiles programs.

On Thursday, a senior North Korean nuclear negotiator called a proposal from Washington to resume denuclearization talks next month “a trick to earn time,” and said North Korea was not interested in negotiating until Washington abandoned its “hostile policy.”

On Friday, both Mr. Esper and Mr. Jeong indicated that the allies were open to changing their plans for a joint air force drill to help maintain diplomatic momentum with North Korea. But they stopped short of canceling the drill.

“We always have to remain flexible in terms of how we support our diplomats to ensure that we do not close any doors that may allow forward progress on the diplomatic front,” Mr. Esper said.

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