Tokyo has also made a decision to remove Seoul from a list of countries with preferential commercial status.
A senior US diplomat said earlier this week that Washington was ready to restart the talks, a day after USA and South Korean militaries ended their regular drills that Pyongyang called an invasion rehearsal.
U.S. diplomats have concluded for years that North Korea had likely produced miniaturised nuclear warheads. "I hope they can do this quickly".
The Pentagon, clearly anxious about the regional security ramifications as another attempt at nuclear diplomacy with North Korea is contemplated, urged South Korea and Japan to "work together to resolve their differences".
Under the pact, originally signed in 2016, the two United States allies directly share military secrets, particularly over North Korea's nuclear and missile capacity. It is automatically renewed annually unless one of the countries decides to pull the plug.
He also said that Japan will continue its requests for South Korea to work to restore bilateral trust.
Tokyo-Seoul ties have been highly strained recently over trade and historical issues.
South Korea said it was terminating the agreement because Japan had brought about "fundamental changes to the environment of security and cooperation between the two countries" by removing the South from a list of trusted trading partners. South Korea has chose to do the same to Japan, with the new rules taking effect in September.
On Thursday, South Korea said it was ending an intelligence-sharing agreement with Japan, further straining ties between Seoul and Tokyo amid a disputed over compensation for forced South Koreans labourers during World War Two. The Japanese government this month canceled South Korea's fast-track trade status. "Regardless, it is important to continue working together in areas that require collaboration", he added.
North Korea has always criticized the joint military exercises of the United States and South Korea, which it considers preparing for a future invasion of its territory.
The pact was significant as a cornerstone of three-way cooperation with the United States, said Yang Uk, a senior research fellow at the Korea Defence and Security Forum in Seoul.
"The ROK government will work to ensure that the latest decision will serve to not weaken the ROK-U.S. alliance, but actually upgrade the alliance so that it becomes even more solid", said Kim Hyun-chong, using the abbreviation for South Korea's official acronym.
Experts said its lapse may slow down the exchange of information because the two countries will have to go through the United States as they did before the pact. "They're supposed to be allies".
"The ROK Ministry of Trade, Industry and Energy also repeatedly requested consultations with the Japanese Ministry of Economy, Trade and Industry with regard to Korea's export control regime that the Japanese side took issues with", Kim said.
The passage of the agreement in 2016 received high praise from then-U.S. President Barack Obama, as it signified major progress toward Washington's long-cherished goal of U.S.
In response, Kang said he also believes extending the GSOMIA is the desirable thing to do but that the government has made a decision to end the agreement.