SEOUL, Jan. 10 (Xinhua) -- South Korean President Moon Jae-in and U.S. President Donald Trump saw possibility for the ongoing talks between South Korea and the Democratic People's Republic of Korea (DPRK) leading to a dialogue between the United Statesand the DPRK, multiple local media reports said Wednesday.

Moon and Trump had a telephone conversation for about half an hour from 10 p.m. local time (1300 GMT), agreeing to strengthen cooperation between the two allies, according to local media citing Seoul's presidential Blue House.

It marked the ninth phone talks between the two presidents since Moon took office in May 2017. During last week's phone conversation, Moon and Trump agreed not to conduct the springtime South Korea-U.S. joint military exercises during the South Korea-hosted Winter Olympics period.

South Korea and the DPRK held the first high-level talks in about two years Tuesday, agreeing to hold a separate dialogue on military affairs. The DPRK agreed to send its athletes and cheering squads to the 2018 Winter Olympics scheduled to kick off on Feb. 9 at South Korea's eastern county of PyeongChang.

During the phone conversation, Moon and Trump saw a possibility that the inter-Korean talks can lead to the U.S.-DPRK dialogue for the denuclearized Korean Peninsula beyond the DPRK's participation in the PyeongChang Winter Olympics.

Trump said he would be open to talks, if the DPRK wants it, at an appropriate time and under right situations.

The U.S. president noted that there would be no military action while the inter-Korean talks go on, dismissing the U.S. media's speculation.

Trump said in last week's phone talks with Moon that he supported the inter-Korean dialogue.