The issue came to the fore with the March 10 dismissal of President Park Geun-hye over allegations she let her close friend meddle in state affairs and colluded with her to extort large sums of money from local conglomerates.

In their second TV debate, former party leader Ahn Cheol-soo and former opposition leader Sohn Hak-kyu voiced opposition to the plan.

"There physically isn't enough time," Ahn, the party founder, said in the debate aired on TV Chosun and co-hosted by Yonhap News TV. "Many people in the National Assembly agree to a constitutional revision, but there needs to be time to agree on the details."

The former software mogul commands the highest approval rating among his party's three contenders and ranks third among all presidential candidates, according to the latest poll by Realmeter.

"More than anything, we must have a public consensus on the issue," he said. "Especially with the heightened standards of the people following the nonviolent, peaceful revolution (that led to Park's ouster), we must reflect the people's opinions."

Ahn proposed the referendum be held during a local election next year.

Sohn, a seasoned politician with followers on the left and right, agreed that it is "unrealistic" to put a constitutional revision to a vote together with the presidential poll.

He suggested instead that the parliamentary committee handling the revision continue its job and a new bill be created to allow the next president to finish the process.

"In that way, the next president should be allowed to become a (so-called) constitutional revision president, and I will become that constitutional revision president," he said.

Vice National Assembly Speaker Park Joo-sun, the third contender, accused his rivals of not even trying to prepare for the referendum, saying he believes it will be possible in May with consent from Ahn and front-runner Moon Jae-in of the Democratic Party.

"The lesson of President Park Geun-hye's impeachment is that hegemonic forces can no longer abuse power and build a country that only fattens their cliques," he said.

The third-largest party in the unicameral parliament is set to nominate its standard-bearer on April 4. (Yonhap)