During his campaign, Moon called for changing the current single-term, five-year presidency into a four-year presidency with the possibility for re-election, limited to two terms, saying that the change would help ensure consistent policy implementation with long-term visions.
The envoy said President Moon was also hoping for an early meeting.
The agreement, struck by Abe and ousted former South Korean President Park Geun-hye, was meant to "finally and irrevocably" settle the matter, with Japan paying 1 billion yen ($9 million at the current rate) to a fund for the women set up by the South Korean government.
With Moon's promise, the political parties are expected to speed up discussions as to how far the revision should go in amending the Constitution, which has been unchanged since 1987, when massive street protests against the military government of Chun Doo Hwan restored a direct presidential election after decades of military rule. An official death toll has never been disclosed. "It is the spirit of the May 18 democracy movement itself". More than 10,000 people attended the commemoration ceremony, the largest ever at the annual event held at the Gwangju cemetery where victims of the clashes are buried.
Moon has picked a former student activist, Im Jong-seok, once accused of being a pro-North Korea sympathizer, as his chief of staff.
Last Friday, President Moon, a former human rights lawyer, issued an order to allow the song to be sung in unison by everyone at the memorial service.More news: Protests Target Both NATO and Trump in Brussels
More news: Jury of 12 chosen for Bill Cosby's indecent assault trial
More news: Often criticized, the Europa League matters once more
During campaign, Moon maintained that the anti-missile system, known as Thaad, should be reviewed by the next administration and the National Assembly, as the previous Park Geun-hye government rushed to approve Thaad's deployment without due process.
Moon, however, will need cooperation from conservative lawmakers to push through his agenda in the fractured parliament, including boosting fiscal spending to create hundreds of thousands of new jobs.
The new president made the remarks during a luncheon meeting with the floor leaders of the ruling Democratic Party (DP), main opposition Liberty Korea Party (LKP), People's Party, Bareun Party and Justice Party, Chung Woo-taik, the LKP whip, told reporters.
It was an extraordinary reversal after Moon's two conservative predecessors attended the memorial event in Gwangju standing while a choir sang "March for the Beloved" and protesters scuffled with security guards.
Abe and the lawmaker also took up a 2015 bilateral agreement on Korean "comfort women", under which the two countries confirmed the longstanding dispute over Korean women forced to work in wartime Japanese military brothels is "resolved finally and irreversibly".
Scrapping the agreement, which he said most South Koreans can not accept, would be another move to erase Park's legacy, who sought to move past the issue that has long plagued ties between the neighbors as they try to forge efforts to end the North Korean nuclear crisis.