Leaders of the ruling and main opposition parties held a second round of talks Tuesday to discuss a way out of the political standoff surrounding the state's alleged interference in last year's presidential election, among other issues, but produced no breakthrough, both sides said.

It marks the second day in a row that the chiefs and floor leaders of the ruling Saenuri Party and the main opposition Democratic Party (DP) failed to reach agreement on key issues dividing the parties, including the DP's demand for a special independent investigation into the election meddling scandal.

The scandal centers on allegations that the state spy agency and other government bodies posted comments online in favor of the then ruling party candidate and now president, Park Geun-hye, ahead of last December's vote.

The ruling party has rejected an independent probe on the grounds that the prosecution is conducting an investigation into the case.

"The two parties' differences over the special committee and special probe remain the same," ruling party spokesman Yoo Il-ho said in a joint press briefing with his DP counterpart Kim Kwan-young.

The spokesman was referring to the DP's demand for a special parliamentary committee tasked with reforming the state spy agency National Intelligence Service.

The two sides clashed over who would chair the committee, whether it should hold legislative powers and the means and level of reform, he added.

"However, (they) agreed to continue discussions and make an effort to reach an agreement," DP spokesman Kim said.

Aside from the election meddling scandal, another key topic of discussion has been the government's 2014 budget.

The budget proposal has been stuck in parliament for weeks as the opposition party has repeatedly boycotted all parliamentary proceedings.

This has prompted concerns that the government may have to draw up a provisional budget for the first time in the country's history.

Prime Minister Chung Hong-won urged the National Assembly to set aside partisan strife, saying a provisional budget would "throw cold water" on the country's economic recovery.

"If the budget proposal isn't passed quickly, the burden will eventually fall on the country's economy and the lives of the people," he said as he presided over a Cabinet meeting.

He also called on the rival parties to pass a set of bills aimed at reviving the economy and creating jobs. (Yonhap News)