South Korea said Tuesday it has agreed with the United States to suspend a major joint military exercise held every August as their tensions with North Korea have significantly subsided following historic summits.

The decision, also announced by Washington, came a week after U.S. President Donald Trump abruptly said following his summit with North Korean leader Kim Jong Un in Singapore that he wants to halt "war games" with South Korea, calling them "tremendously expensive" and "very provocative."

All planning activities for the Ulchi Freedom Guardian exercise have been suspended, the defense ministries of the two countries said.

Coupled with Trump's suggestion of scaling down U.S. forces in South Korea, the suspension could strengthen concerns among Washington's allies in Asia over whether it would sustain a pivotal role in the region's security architecture.

"There is no impact on Pacific exercises outside of the Korean Peninsula," the Pentagon said in a statement as it announced the suspension of the annual exercise. "We are still coordinating additional actions. No decisions on subsequent war games have been made."

Trump said after the Singapore meeting that joint military exercises with South Korea could be halted as long as North Korea continues denuclearization talks in good faith.

North Korea has long denounced military exercises between the two countries as a rehearsal for invasion and tensions around the Korean Peninsula have escalated when they are conducted.

Choi Hyun Soo, a spokesman for South Korea's Defense Ministry, told reporters that the two countries hope to see some concrete actions from North Korea following their latest decision.

Pentagon spokeswoman Dana White said Defense Secretary Jim Mattis, Secretary of State Mike Pompeo and national security adviser John Bolton will meet later this week to discuss the next moves.

On Monday, Pompeo said he is likely to make yet another visit to North Korea "before too terribly long" to follow up the unprecedented summit on June 12.

"We still have to flesh out all the things that underlay the commitments that were made that day in Singapore," Pompeo said at an event in Detroit.

When he met with Trump, Kim also committed to "complete" denuclearization of the Korean Peninsula, which he first promised during a summit with South Korean President Moon Jae In in late April.

But the agreement between the U.S. and North Korean leaders lacked details on how to proceed toward that goal.

Ulchi Freedom Guardian is a largely computer-simulated command post exercise that last year involved 17,500 U.S. service members, with 3,000 coming from outside South Korea. They were joined by some 50,000 South Korean troops and hundreds of thousands of South Korean government personnel all the way up to the Cabinet level.

U.S.-led United Nations Command forces from seven other countries -- Australia, Britain, Canada, Colombia, Denmark, New Zealand and the Netherlands -- also have participated.

Besides that exercise, another large one, Key Resolve, is held each spring, while numerous smaller ones also take place.

South Korea and the United States have claimed that their regular military exercises, such as Max Thunder that ran for two weeks through late last month, are defensive in nature.

Currently, the United States has about 28,000 soldiers in South Korea.

In 1994, the United States and South Korea canceled their long-running military exercise known as Team Spirit on the premise that North Korea would freeze its nuclear development program in return for economic assistance under the Agreed Framework.

Trump's intention to halt the military exercises was immediately welcomed by China after he announced it during a post-summit press conference in Singapore.

For years, China has said the "root cause" of the North Korean nuclear issue stems from disagreements between Washington and Pyongyang.

When tensions were extremely high until this year over North Korea, China advocated the idea of the so-called "double suspension" -- simultaneously freezing Pyongyang's nuclear program and Washington-Seoul military exercises.

On Tuesday, China's official media said that the North Korean leader will make a two-day visit to Beijing.