"South Korea is a wealthy country and could and should pay more to help offset the cost of defense", Esper said in a press conference following the meeting.
South Korea had proposed talks with North Korea on how to handle its facilities in the resort, once a rare example of cooperation between the Koreas, after North Korean leader Kim Jong Un said last month he wanted them removed amid cooled inter-Korean relations.
North Korea said on Thursday it had turned down a USA offer for fresh talks, saying it was not interested in more talks merely aimed at "appeasing us" ahead of a year-end deadline Pyongyang has set for Washington to show more flexibility in negotiations.
North Korea said in a commentary from state media KCNA on Friday that the USA demand for a greater South Korean contribution to defense costs was an attempt to "exploit" and tighten its control over South Korea.
"It is important to note that most of the money (that South Korea contributes) stays here in the country, easy over the 90% of the funding stays here in Korea, it does not go to the United States", he said in an apparent bid to persuade not just Korean officials, but al so tax payers that their money wasn't being used to fund things unrelated to South Korean security.
On his flight to South Korea, Esper did say the USA was seeking a "substantial increase" in Seoul's contribution, but he wouldn't be any more specific.
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A South Korean lawmaker said last week that US officials demanded up to $5 billion a year, more than five times what Seoul agreed to pay this year under a one-year deal.
Seoul now contributes under $1 billion (€907 million) a year for USA military support which began in 1951 during the three-year war between the two Koreas.
Jeong said he shared the view with Esper that the cost-sharing pact should be fair and mutually agreeable, according to the Yonhap News Agency, but neither official gave specific figures.
North Korea has given the United States until the end of the year to come up with a new approach to denuclearization talks, and it threatened this week to reverse an earlier decision to end nuclear and intercontinental ballistic missile tests.
A survey by the government-affiliated Korea Institute for National Unification released last week showed 96% of South Koreans opposed paying more for the USA military presence.
He plans to hold bilateral talks with the South Korean defense minister on the sidelines Sunday.
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After his talks with Jeong, Esper warned that South Korea's decision to end an intelligence-sharing pact with Japan, called GSOMIA, would impact military readiness - presumably by slowing the ability of the US allies to directly share information about North Korean military activity.
"The only ones who will benefit from expiration of GSOMIA and continued friction between Seoul and Tokyo are Pyongyang and Beijing", the Pentagon chief said.
A spokeswoman for the U.S. State Department said Trump remained committed to making progress on agreements he reached with Kim Jong Un at a first summit in Singapore in June past year, namely "transformed relations, building lasting peace, and complete denuclearisation".
The defense secretary also called for Seoul to maintain an intelligence-sharing pact with Washington's other Asian ally, Japan, that Seoul is about to let lapse.
The neighbors are embroiled in a trade row stemming from long-running disputes over wartime history, and Seoul announced in August it would terminate the General Security of Military Agreement (GSOMIA) when it expires next week.
The moves are seen as retaliation against South Korean Supreme Court rulings past year that ordered Japanese companies to pay compensation to South Korean victims of forced labor during Japan's colonial rule over the Korean Peninsula.
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