The unexpected telephone conversation was made on the eve of a historic summit between Trump and North Korean leader Kim Jong-un in Singapore.
Both Trump and Kim arrived in Singapore on Sunday.
President Moon expressed hope for the success of the unprecedented US-North Korea summit, telling his US counterpart that all other South Koreans will pray for its success, Cheong Wa Dae spokesman Kim Eui-kyeom told a press briefing.
The South Korean president said the Trump-Kim summit, if it succeeds, will be a "gift" to the entire world, according to Kim.
"President Moon and President Trump agreed Trump and Kim will be able to make a great achievement if the two leaders come together to find a common denominator through frank discussions," the Cheong Wa Dae spokesman said.
Trump said he will also send his Secretary of State Mike Pompeo to Seoul immediately after his Singapore summit with Kim to explain the outcome of the first-ever US-North Korea summit.
The US president said he will also closely discuss ways to implement the outcome of the US-North Korea summit with President Moon, Kim said.