Trump appears to be intent on thawing relations with North Korea for now, amid the upcoming 2018 Winter Olympics in South Korea next month, where North Korea has agreed to send athletes and a delegation to participate.
According to a readout of the call, "President Trump expressed his openness to holding talks between the United States and North Korea at the appropriate time, under the right circumstances".
The talks were held for the first time since 2015 and Moon credited Trump for sparking them, according to Reuters.
North Korea and South Korea held talks on Tuesday after a prolonged period of tension on the Korean peninsula over the North's missile and nuclear programmes. North Korea agreed to send athletes to the games after talks with Moon's government on January 9.
The Kremlin strongman congratulated the North Korean dictator, saying he had won the latest stand-off with the US and South Korea.
Rising tensions between the United States and North Korea, which conducted its largest nuclear test in September and fired off a powerful ICBM in late November, have raised concerns worldwide.
South Korea's president added that improving inter-Korean ties is dependent on the North being willing to abandon its controversial nuclear weapons program.
Tuesday's meeting will come a week after the first conversation in two years between officials from North Korea and South Korea. Representatives of the Democratic People's Republic of Korea (DPRK), known as North Korea, and South Korea should handle the issues between Pyongyang and Seoul, North Korea's Ambassador to Russia Kim Hyung Jun said at a reception for the Russian media on Wednesday.
But the president added that the talks wouldn't necessarily be held without preconditions, saying that Kim "knows I'm not messing around".
Asked if he had spoken to Kim, Trump said "I don't want to comment on it".
The two Koreas released a joint statement saying, "South and North Korea have chose to make joint efforts for the unity of the people and reconciliation by establishing an environment for peace and easing military tensions on the Korean Peninsula".
"Without our attitude, that would have never happened", Trump said.
During his interview with The Wall Street Journal, Trump acknowledged that recent talks between the two Koreas may be an attempt to drive a wedge between South Korea and the United States. Trump has denied pursuing a "bloody nose" strategy and agreed with South Korea to delay an annual joint military exercise that was scheduled to take place during the Winter Olympics.