‍U.S. President Donald Trump reaffirmed his commitment to resolving the nuclear issue of the Democratic People's Republic of Korea (DPRK) through dialogue Thursday, hours after his second summit with the DPRK leader Kim Jong Un ended without an agreement, according to Yonhap.

The remarks were made during a phone call between Trump and president of the Republic of Korea (ROK) Moon Jae-in while Trump was on board Air Force One en route to the U.S., Yonhap reported. 

At a press conference held by Trump and the U.S. Secretary of State Mike Pompeo earlier the same day in Hanoi, Trump said he had walked away from a nuclear deal at his second meeting with Kim because he had made unacceptable demands on lifting U.S.-led sanctions.

The Yonhap report also mentioned that in the telephone conversation between Trump and Moon, the U.S. president asked Moon to "actively" help mediate future dialogue with Kim. 

For Moon's part, he expressed hope for progress in the future. "While saying he wished for President Trump's continued determination and efforts to end the world's last remaining Cold War conflict and confrontation on the Korean Peninsula, President Moon said we will do all we can under the close cooperation between South Korea (the ROK) and the U.S.," Yonhap cited the spokesman for the Blue House as saying.

Moon suggested he and Trump meet in the near future to continue their discussions, which Trump agreed to, according to Yonhap. 

Earlier the ROK's presidential office, known as the Blue House said it regretted that no deal was reached at the Trump-Kim summit, but the two sides had made meaningful progress.

The ROK's presidential office, known as the Blue House, said in a statement Trump and Kim made "more meaningful progress than ever", and Trump's willingness to continue dialogue would brighten prospects for another meeting.

Yonhap also reported that the ROK's political parties on Thursday also expressed regret over the outcome of the Kim-Trump summit.

According to Yonhap, the ruling Democratic Party (DP) expressed hopes that Washington and Pyongyang could meet again as soon as possible.

The main opposition Liberty Korea Party (LKP), which has called on the DPRK to give up nuclear weapons in a complete, verifiable and irreversible manner, also expressed disappointment, Yonhap reported, saying the party also urged negotiations to be resumed as soon as possible. 

While regret seems to be the dominant reaction from the political circle of the ROK, the Yonhap report also mentioned that the minor opposition Bareunmirae Party described the summit as "productive pain" needed to move toward complete denuclearization of the Korean Peninsula. 

The minor liberal Party for Democracy and Peace also called on the Moon Jae-in administration to play an active role in facilitating a potential third summit between Trump and Kim, according to Yonhap.

(With inputs from Reuters)