North Korea has agreed with the United States on the importance of "step-by-step and simultaneous action," its state-run media said Wednesday, laying bare differences between the two nations over the pace of Pyongyang's denuclearization process.

A joint statement signed by U.S. President Donald Trump and North Korean leader Kim Jong Un at their summit in Singapore on Tuesday did not mention "complete, verifiable and irreversible denuclearization," a concept U.S. Secretary of State Mike Pompeo has said would be the only outcome Washington will accept.

Trump and Kim in their statement "shared recognition to the effect that it is important to abide by the principle" of step-by-step action to achieve denuclearization of the Korean Peninsula, the Korean Central News Agency said.

As the United States has called on North Korea to give up all its nuclear weapons swiftly and verifiably, negotiations between the two countries are likely to face a rocky road over how to attain the goal of eliminating nuclear weapons from the divided peninsula.

To follow up on the summit, U.S. officials will hold talks with N. Korea next week, Trump said at a press conference after the first-ever summit between a sitting U.S. president and a North Korean leader.

Kim is believed to opt for "phased and synchronous measures" so Pyongyang can win rewards for every step it takes in the denuclearization process.

KCNA said Wednesday that during the summit, Trump expressed his intention to suspend joint military drills between the United States and South Korea -- drills the North has denounced as preparations for invasion -- over a period of "good-will dialogue" with Pyongyang.

The U.S. president also promised to offer security guarantees to Pyongyang from Washington and lift sanctions against North Korea "along with advance in improving the mutual relationship through dialogue and negotiation," the news agency said.

If the United States takes "genuine" steps to build trust to improve relations with North Korea, Pyongyang can continue to implement "additional good-will measures of next stage," Kim was quoted by KCNA as telling Trump.

Kim urged Trump to make a "bold decision" to halt "irritating and hostile military actions against each other," while they accepted invitations of each other to visit Pyongyang and Washington, according to the news agency.

On Tuesday, the two leaders signed a joint document that includes Pyongyang's commitment to "complete denuclearization" and Washington's pledge to provide it with security guarantees. KCNA reported the same document on Wednesday.

But both the document and the official news agency report did not mention whether Trump and Kim at their meeting discussed the issue of North Korea's abductions of Japanese nationals in the 1970s and 1980s.