File Photo: Top leader of the Democratic People's Republic of Korea (DPRK) Kim Jong Un (R) and U.S. President Donald Trump take a walk during their summit meeting in Singapore on June 12, 2018. (Xinhua/Ministry of Communication and Information of Singapore)

NEW YORK, Sept. 26 (Xinhua) -- U.S. Secretary of State Mike Pompeo said here on Wednesday that he has had a "very positive" meeting with the Foreign Minister of the Democratic People's Republic of Korea (DPRK), Ri Yong Ho, to discuss the next summit between the two countries' top leaders.

Pompeo tweeted that he had a "very positive meeting with #DPRK Foreign Minister Ri Yong Ho @UNGA to discuss upcoming summit & next steps toward denuclearization of #NorthKorea."

"Much work remains, but we will continue to move forward," he noted.

Also on Wednesday, Pompeo said in an interview with CBS News in New York that he will soon "personally be traveling to Pyongyang."

Speaking of the time of the meeting between U.S. President Donald Trump and the DPRK's top leader, Kim Jong UN, Pompeo said the meeting "may happen in October, but more likely sometime after that."

"It takes a little while to put these together, and we want to make sure we've got the conditions just right so the two leaders can be successful," he noted.

South Korean President Moon Jae-in said here on Tuesday that U.S. President Donald Trump and the top leader of the Democratic People's Republic of Korea (DPRK), Kim Jong Un, could meet before the end of this year.

Trump said Tuesday that his second summit with Kim will be announced "pretty soon," yet the summit is likely to take place in a different place.

At the conclusion of the historic Trump-Kim summit in June in Singapore, the two sides issued a joint statement, agreeing to improve bilateral relations and work together to build a lasting and stable peace regime on the peninsula.

However, U.S.-DPRK talks have been stuck in an impasse due to their differences over the scale of denuclearization, U.S. sanctions, and whether to issue a war-ending declaration.

In August, just one day after Pompeo announced his visit to the DPRK, Trump tweeted that he had asked Pompeo not to go due to the insufficient progress with the DPRK.

During his Sept. 18-20 trip to Pyongyang, Moon held talks with Kim, and signed the Pyongyang Declaration, an advancement towards the Korean Peninsula's denuclearization and concrete measures to end hostile acts near the inter-Korean border areas.

Pompeo said later in response that the United States is ready to transform its relations with the DPRK immediately.

He added that he had invited Ri Yong Ho to meet in New York City where they were scheduled to attend the United Nations General Assembly meeting.