U.S. President Donald Trump said on Tuesday that there was progress on the Korean Peninsula issue after the Democratic People's Republic of Korea (DPRK) expressed willingness to denuclearize the peninsula.

"They seem to be acting positively. We're going to see," said Trump before meeting at White House with visiting Swedish Prime Minister Stefan Lofven.

The South Korean presidency said earlier on Tuesday that Pyongyang showed willingness to talk "candidly" with the United States on issues including denuclearization of the Korean Peninsula and normalization of ties with Washington.

The DPRK also agreed with South Korea to hold the third inter-Korean summit talks in late April.

The positive moves came as a result of the two-day visit to Pyongyang by South Korean President Moon Jae-in's special delegation led by Chung Eui-yong, Moon's top national security adviser.

"It would be a great thing for the world. It would be a great thing for North Korea (DPRK)," said Trump of the positive momentum on the Korean Peninsula issue.

"We have made progress, there's no question about it," he added. "I'd like to be optimistic."

When asked by reporters if the United States was ready for direct talks with the DPRK, Trump just cautiously said: "We're going to see what happens."

In a tweet on Tuesday morning, Trump recognized "possible progress" made on the Korean Peninsula issue with a reserved attitude.

"May be false hope, but the U.S. is ready to go hard in either direction," he added in the tweet.

U.S. Vice President Mike Pence kept a harsh rhetoric on the DPRK, saying that the U.S. "maximum pressure" strategy against Pyongyang to seek an end to its nuclear program will continue.

"All options are on the table and our posture toward the regime (the DPRK) will not change until we see credible, verifiable, and concrete steps toward denuclearization," Pence said in a statement on Tuesday.