SEOUL (Reuters) - South Korea on Monday proposed military talks with North Korea, the first formal overture to Pyongyang by the government of President Moon Jae-in, to discuss ways to avoid hostile acts near the heavily militarized border.

There was no immediate response from North Korea to the proposal for talks later this week. The two sides technically remain at war but Moon, who came to power in May, has pledged to engage North Korea in dialogue as well as bring pressure to impede its nuclear and missile programs.

The offer comes after North Korea claimed to have conducted the first test of an intercontinental ballistic missile (ICBM) earlier this month, and said it had mastered the technology to mount a nuclear warhead on the missile.

“Talks and cooperation between the two Koreas to ease tension and bring about peace on the Korean peninsula will be instrumental for pushing forth a mutual, virtuous cycle for inter-Korea relations and North Korea’s nuclear problem,” South Korea’s Unification Minister Cho Myoung-gyon told a news briefing.

The United States, South Korea’s main ally, which has been trying to rally international support for tougher sanctions on North Korea, appeared cool to the proposal, recalling President Donald Trump’s statements that conditions must be right for dialogue.

“I think the President has made clear in the past with respect that any type of conditions that would have to be met are clearly far away from where we are now,” White House spokesman Sean Spicer told a news briefing.

The South Korean defense ministry proposed talks with the North on July 21 at Tongilgak to stop all activities that fuel tension at the military demarcation line.

Tongilgak is a North Korean building at the Panmunjom truce village on the border used for previous inter-Korea talks. The last such talks were held in December 2015.

Cho also urged restoration of cross-border military and government hotlines that North Korea cut last year in response to South Korea’s imposition of new economic sanctions after a nuclear test by Pyongyang.

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South Korea also proposed separate talks by the rival states’ Red Cross organizations to resume a humanitarian project to reunite families separated during the 1950-53 Korean War.

The South Korean Red Cross suggested talks be held on Aug. 1, with possible reunions over the Korean thanksgiving Chuseok holiday, which falls in October.

The last such reunions were in October 2015.

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China, which has close ties to Pyongyang despite its anger over North Korea’s missile and nuclear tests, welcomed the proposal, saying cooperation and reconciliation could help ease tensions.

“We hope that North and South Korea can work hard to go in a positive direction and create conditions to break the deadlock and resume dialogue and consultation,” Chinese Foreign Ministry spokesman Lu Kang told a daily news briefing.

The proposals come after Moon said at the G20 summit in Hamburg this month he was in favor of dialogue despite the “nuclear provocation” of North Korea’s latest missile test.

When Moon visited Washington after being elected president, he and Trump said they were open to renewed dialogue with North Korea but only under circumstances that would lead to Pyongyang giving up its weapons programs.

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“The fact that we wish to take on a leading role in resolving this (North Korean) issue has already been understood at the summit with the United States and the Group of 20 summit meetings,” Cho said on Monday.

In the proposal for talks, South Korea did not elaborate on the meaning of hostile military activities, which varies between the two Koreas. South Korea usually refers to loudspeaker propaganda broadcasts by both sides, while North Korea wants a halt to routine joint U.S.-South Korea military drills.

Moon suggested this month that hostile military activities at the border be ended on July 27, the anniversary of the 1953 armistice agreement. Since no truce was agreed, the two sides remain technically at war.

Asked if South Korea was willing to be “flexible” on military drills with the United States should North Korea be open to talks, Cho said the government had not discussed the matter specifically.

Pyongyang has said it will not engage in talks with Seoul unless it turns over 12 waitresses who defected to South Korea last year after leaving a North Korean restaurant in China.

North Korea says South Korea abducted the waitresses, but Seoul has said they defected of their own free will. Cho said this matter was not included on the talks agenda.