South Korea's rival political parties failed to reach an agreement on extending the ongoing parliamentary probe into the fatal Itaewon crowd crush and convening an extraordinary session in January.

Main opposition Democratic Party(DP) floor leader Park Hong-keun put forth the two proposals during talks with his ruling People Power Party(PPP) counterpart Joo Ho-young on Tuesday, but they came away without striking a deal.

Following the meeting, Joo said the two sides plan to continue talks on the probe extension after listening to opinions of members on the Itaewon investigation panel, which was initially tasked with probing the tragedy through January 7.

However, the PPP floor leader said his party will not accept the proposed extra session to handle bills the two sides have yet to agree on.

The DP has called for the chamber to handle livelihood bills, including the one aimed at extending a freight rate system guaranteeing truckers' basic wages.

The ruling bloc suspects the main opposition is attempting to protect party leader Lee Jae-myung from indictment by abusing lawmakers' immunity from arrest while the Assembly is in session. Lee has been summoned for questioning by the prosecution over third-party bribery allegations.