The United States had initially demanded a doubling of the South Korean contribution, but in the end had to settle for an increase of 8.2 percent for the first year, equivalent to the rise in Seoul’s total defense budget this year. South Korea has agreed to pay 1.0389 trillion won, or around $920 million, up from the 960 billion won a year it paid from 2014 to 2018.

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The United States and South Korea expressed satisfaction with the deal, known as the Special Measures Agreement, or SMA.

“The United States government realizes that Korea does a lot for our alliance and for peace and stability in this region, and the SMA is only a small part of that,” said Timothy Betts, U.S. deputy assistant secretary of state for plans, programs and operations, who led the negotiations.

“But it’s an important part, and we are pleased that our consultations resulted in an agreement that I think will strengthen transparency and strengthen and deepen our cooperation in the alliance.”

The signing was labeled “preliminary” because the deal needs to be ratified by South Korea’s legislature. Foreign Minister Kang Kyung-wha expressed optimism that it would be approved.

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“I think the response so far has been quite positive,” she told ­Betts. “Of course there are some points of criticism as well, and we will have to deal with them, but I think at this point we were able to close the gap on the total amount.”

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The two sides held 10 rounds of negotiations last year, failing to reach agreement before the previous deal expired at the end of 2018.

They agreed to set up a working group to handle cost-sharing negotiations in the future, stipulating that if no new agreement is reached by the end of this year, “to prevent the absence of an agreement, the two sides can extend the previous agreement upon mutual consent.”

Opposition conservative lawmaker Won Yoo-chul said the two sides had reached a “wise” and reasonable compromise.

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“It is fortunate that the deal was reached before the upcoming Trump-Kim summit in Vietnam, so that the troops card is off the table,” he said. “Defense cost-sharing is an issue between us two allies, not a bargaining chip with North Korea.”

But Won, a member of the parliamentary foreign affairs committee, warned that the short-term nature of the deal could cause friction.

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“With renegotiation every year, the two sides will go through a standoff each time, which will look bad for the alliance,” he said. “The alliance between two countries should not be approached from an economic perspective alone.”

Ruling party lawmaker Song Young-gil said the two sides had little choice but to reach a deal before the summit. He said he expects the United States to push harder in the next round of negotiations, so that the president can declare a “win” ahead of elections in 2020.

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“The way Washington views the alliance has changed since Trump took office,” he said. “With Trump’s isolationist pursuits, the United States is not taking the role of global policeman anymore.”

The deal has also been closely watched in Japan, which is next in line in Trump’s campaign against what he sees as “free-

riders” taking advantage of U.S. defense spending.

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Although senior members of his administration have repeatedly tried to convince Trump that the United States gains enormous national security benefits by stationing troops in Japan and South Korea, the president is determined to get more from both countries, especially because both run trade surpluses with the United States.

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South Korea hosts about 28,500 U.S. troops on more than 20 sites, while Japan hosts around 54,000, about half of them on the island of Okinawa.

Michael Bosack, a special adviser at the Yokosuka Council on Asia-Pacific Studies in Japan, said the agreement with South Korea would reassure U.S. allies that a deal is possible with the Trump administration. But he warned that U.S. brinkmanship tactics have already fueled doubts about the country’s commitment to its allies.

“While in the short-term, this may mean allies pay more for things like cost-sharing measures, in the long-term it erodes trust in U.S. security guarantees, which bears far more significant costs,” he said.

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If the United States is seen as “extortionist” in the negotiations, it could undermine public support for the alliance in South Korea, he said.

Japan is due to begin negotiations over defense cost-sharing at the end of this year or early next year. Tokyo will argue that it is anything but a “free-rider,” especially because it is making significant purchases of F-35s and the Aegis Ashore missile defense system from the United States. But Bosack said those purchases won’t show up directly in the troop cost-sharing balance sheet.

“If Japanese officials are counting on those things alone to carry them through cost-sharing negotiations, they are in for a rude awakening,” he said.

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Meanwhile, the United States and North Korea plan to hold a new round of talks in another Asian nation next week, as they prepare for the Trump-Kim summit, South Korea’s presidential office announced Sunday.

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