The foreign chiefs of the United States, Japan and South Korea expressed expectations Thursday for substantial progress on North Korea's denuclearization, aiming to work together in a process that U.S. Secretary of State Mike Pompeo said may not be easy.

As the foreign chiefs reaffirmed the importance of trilateral cooperation, Pompeo said the United States is committed to "complete, verifiable, and irreversible" denuclearization of the Korean Peninsula.

Pompeo, who has led U.S. negotiations with North Korea, said its leader Kim Jong Un understands "the urgency" of denuclearization of the peninsula, adding that sanctions on the North will not be lifted until it denuclearizes as the sequence is important.

"The U.S. alliances with these two countries are absolutely ironclad," Pompeo said at a joint press conference with Japanese Foreign Minister Taro Kono and South Korean Foreign Minister Kang Kyung Wha.

Despite what U.S. President Donald Trump hailed as a "comprehensive" agreement reached with Kim, details such as how North Korea will denuclearize have yet to be worked out.

Differences over the pace of the denuclearization process apparently remain, as North Korea's state media has reported Trump and Kim agreed on the importance of "step-by-step and simultaneous action."

Speaking at the same press conference, Kang described the June 12 summit between Trump and Kim in Singapore as a "beginning" for a peaceful and denuclearized Korean Peninsula, adding the three ministers hope Pyongyang will start taking concrete action.

In the document released Tuesday, the United States promised to provide security assurances to North Korea, which committed it would "work toward complete denuclearization."

For Japan, resolving the issue of North Korea's past abductions of Japanese nationals in the 1970s and 1980s is also critical, a point Prime Minister Shinzo Abe has explained to Trump.

Japan aims to arrange an Abe-Kim summit in September, a Japanese government source said Thursday. But Kono warned there was no point in just holding a dialogue.

Kono added any summit between Japan and North Korea should produce progress in resolving outstanding issues including Pyongyang's past abductions of foreign nationals.

(From left: Pompeo, Kang and Kono)

The trilateral framework is critical as Japan and South Korea -- both key U.S. allies in Asia -- have faced similar threats from North Korea's nuclear and missile development programs in recent years.

Trump's announcement after Tuesday's summit that he will stop "war games" with South Korea has continued to reverberate in Seoul and Tokyo.

North Korea has demanded that the United States and South Korea stop joint military exercises, which it views as preparations for an invasion.

"We understand that any pause in (joint U.S.-South Korea military) exercises is contingent on the DPRK's action for denuclearization," Kono said, using the acronym for the Democratic People's Republic of Korea.

Under the Abe administration, Japan has been seeking closer coordination with the United States and beefing up its defense capabilities, citing the North Korean threat.