Moon suggested the parliament propose multiple candidates for the position of prime minister and the president select the country's No. 2 official from among them.
"Let's allow people to vote on this proposal during the 2020 general election and discuss ways to pass a proposed constitutional revision that will take effect starting from the next administration," Moon said.
He made the remarks during his speech to mark the 100th anniversary of the establishment of the provisional legislative body during Japan's 1910-45 colonial rule.
In March, President Moon Jae-in submitted a constitutional revision bill that calls for changing the current single five-year presidential term to a maximum of two successive four-year terms.
But in May, opposition parties boycotted a parliamentary vote on the motion.
South Korea's Constitution was last revised in 1987 after decades of military-backed authoritarian rule. The current single, five-year presidential term was then adopted, together with a direct presidential election system.
But the current system has been criticized for concentrating too much power in the presidency.
"As it is hard to hold a referendum only for a constitutional revision bill, the speaker thinks it would be good for the country to put that to a vote in tandem with the general elections," Lee Kye-sung, a parliamentary spokesman, said.
Currently, the president names the prime minister. The prime minister is officially the No. 2 official of the government, but the post is largely symbolic as the president makes key decisions.
Lee said if the prime minister is recommended by parliament and appointed by the president, he or she will be able to work with more responsibility and authority. (Yonhap)