WASHINGTON, June 14 (Xinhua) -- The United States and South Korea have agreed to work together to fulfill U.S. President Donald Trump's "guidance" on the joint military exercises, said Pentagon on Thursday.

Trump, after a historic meeting with Kim Jong Un, top leader of the Democratic People's Republic of Korea (DPRK) on Tuesday, told reporters that he will halt the annual U.S. war games with South Korea as Washington was in talks with Pyongyang which has constantly denounced the drills.

Pentagon said in a statement that U.S. Secretary of Defense James Mattis spoke over phone with his South Korean counterpart Song Young-moo on Thursday, discussing the results of the U.S.-DPRK summit.

Mattis and Song also "discussed their mutual support to ongoing diplomatic efforts, to include how we are working together to fulfill the President's guidance on U.S.-ROK (South Korea) combined military exercises," the statement added.

In an almost one-hour press conference on Tuesday, Trump said the joint military exercises, usually conducted each spring and summer in South Korea, will be stopped "unless and until we see the future negotiation (between the United States and the DPRK) is not going along like it should."

Trump also called the drills "very expensive" and "provocative."

Harry Harris, a retired Navy admiral whom Trump has picked as the next U.S. ambassador to South Korea, endorsed Trump's decision to halt the joint military exercises.

"We should give major exercises a pause to see if Kim Jong Un is serious about his part of the negotiations," Harris told a Senate hearing to consider his nomination on Thursday.

South Korean President Moon Jae-in said on Thursday that he will carefully review the joint military exercises if talks between the DPRK and the United States continue.