The General Security of Military Information Agreement, set to expire at midnight Friday, is seen by Washington as a key platform for trilateral security cooperation against North Korea's nuclear threat and China's military rise.
"My message to them was, look, I understand the historical issues. I understand the recent items that prompted it, but we have far greater concerns, if you will, that involve Pyongyang and Beijing, and we have to move forward," Esper told reporters in Vietnam, apparently referring to his meetings with his South Korean and Japanese counterparts in the past week.
"That requires leadership from both countries, and the United States -- I, in this case -- will do what we can to push it forward," he said, according to a transcript provided by the Pentagon.
Esper's trip to Asia came as Seoul and Washington have been in tense negotiations over sharing the costs for the upkeep of 28,500 American troops in the South. A news report earlier said that Washington is considering pulling some American troops from South Korea unless Seoul sharply raises its share.
Esper rejected the report.
"We're not threatening allies over this," Esper said. "This is a negotiation. The State Department has the lead. Let's let them sit down with their counterparts and work through this, as allies should, privately and work through the details."
He disagreed with the characterization of the current situation as a "rift" between Seoul and Washington, saying the US has been pressing allies in Europe and other parts of the world to improve their burden sharing.
"I don't think it's unreasonable to ask countries who have the means to contribute more to their own defense and to the cost sharing of United States presence to do more," he said.
Esper also said he has no regrets about postponing military exercises between South Korea and the United States, even though North Korea snubbed the gesture as meaningless to efforts to revive diplomacy between Washington and Pyongyang.
"I saw the one response they made was not as positive as we would like, obviously, and that's disappointing," he said. "But I don't regret trying to take the high road, if you will, and keep the door open for peace and diplomacy if we can move the ball forward."
South Korea and the US announced Sunday they were postponing planned air exercises to support diplomatic efforts to denuclearize the North.
The next day, a senior Pyongyang official dismissed the move as "not helpful" and demanded the US end its military exercises with the South.
"We keep saying the end of the year will be the time by which at least the North Koreans have stated they may move in a different direction, so I think we've got to keep pressing forward," Esper said. "I think it's too important not to keep trying."
The secretary was referring to North Korea's demands that the US come up with an acceptable offer before the end of the year.
The two sides have been apart on how much the North should denuclearize in order to receive sanctions relief and other concessions from the US.
Asked if he expects the North to revert to provocative behavior, including missile tests, Esper refused to speculate.
"We'll see," he said. "Like I said, our decision to postpone the exercise was a gesture of goodwill, and my clear ask for them was to do the same; show us that you're serious, that you also want to act in good faith and suspend your exercises ... So I think the ball is in their court." (Yonhap)