The main opposition party proposed Sunday the creation of a trilateral dialogue channel with the ruling party and bereaved families of April's deadly ferry sinking to shed light on what caused the tragedy.

The move comes after the families of the victims on Tuesday rejected a bipartisan deal to pass a special bill aimed at uncovering the details of the disaster, insisting that the ruling party should not be allowed to select any of the seven-member panel to be tasked with choosing a special counsel.

The Sewol ferry capsized off southwestern South Korea on April 16, leaving more than 300 people, mostly high school students, dead or missing.

"There has been some progress on how to form an investigative committee for the tragedy, but more efforts seem to be needed as the victims' families see the progress as inadequate," said Park Young-sun, interim chief and floor leader of the main opposition party New Politics Alliance for Democracy (NPAD).

"Now is the time for the bereaved families and heads of the rival parties to have dialogue together. The ruling Saenuri Party should decide whether to accept our proposal on the trilateral channel."

In accordance with the law, the ruling and main opposition parties each select two members for the panel, which then recommends two special counsel candidates to the president. The president appoints one of the two.

Seoul Mayor Park Won-soon and South Chungcheong Province Governor An Hee-jung, who are both NPAD members, called for President Park Geun-hye to resolve the issue of the ferry sinking "actively and sincerely."

"The ruling party and the presidential office should deal with this issue sternly and aggressively. If not, there will be no political progress and the general public will face division and sorrow," the mayor said.

The provincial governor made a similar claim, urging President Park to accept any demand from the bereaved families and the opposition party.

The victims' families have requested President Park to have a meeting with them in a bid to call for the enactment of the special bill, while some of them have staged a rally in front of the presidential office.

A father who lost his daughter in the disaster has been hospitalized since Friday following a 40-day hunger strike aimed at securing an independent probe.

The government has been accused of bungling its initial response to the accident, one of the nation's worst maritime disasters. (Yonhap)