SEOUL, Dec. 1 (Xinhua) -- Rift deepened among South Korean politicians over how to let President Park Geun-hye resign after the embattled leader's third address to the nation in which she threw the ball of decision on her fate to parliamentary court.

Choo Mi-ae, chairwoman of the biggest opposition Minjoo Party, and former ruling Saenuri Party chairman Kim Moo-sung who is leading the anti-Park faction in his party met on Thursday to discuss the way of removing the scandal-hit president from office, according to local media reports.

The meeting was held at the chairwoman's suggestion, but the political big shots failed to reach any agreement on detailed schedules and legal procedures for the president's resignation which Park demanded in her speech on Tuesday.

Addressing the nation for the third time since the scandal involving herself emerged in October, Park said she will defer her retreat, including the shortening of presidency, to the unicameral parliament.

Under the country's constitution, impeachment and constitutional amendment are the only options to cut short Park's single, five-year term as the scandal-plagued leader refused a voluntary resignation citing the breach of the constitution that guarantees a full tenure except treason and insurrection.

The former Saenuri chief reportedly said his anti-Park faction would vote on a bill to impeach Park unless the president accepts the faction's call to voluntarily resign by next April, but he indicated no need for impeachment vote if Park accepts it.

Choo stressed the importance of the impeachment motion to be passed through the National Assembly as late as next Friday when the regular session ends. The main opposition party head demanded Park step down by the end of next January.