"There were discussions about the bills that were not dealt with in late August," Rep. Hong Young-pyo, floor leader of the ruling party, told reporters after the meeting. "We agreed to complete remaining procedures at each parliamentary committee and handle the bills on Sept. 20."

Hong's LKP counterpart, Rep. Kim Sung-tae, also said that the rival parties reached agreement on handling those bills as a package.

The current banking law prevents nonfinancial firms owning more than a 4 percent stake in a bank, and the government of President Moon Jae-in and the ruling party want to ease the ownership limit for Internet-only banks.

The main opposition LKP agrees on raising the cap, but it wants to boost the limit higher.

The current restriction on bank ownership is aimed at preventing family-owned conglomerates gaining control of lenders on concerns that they could easily get credit for their expansions.

Two Internet-only banks -- K-Bank and Kakao Bank -- were launched last year, but they have faced difficulty finding sustainable growth, as their two biggest shareholders, KT and Kakao, are unable to issue shares to increase the banks' capital.

Other issues to be dealt with in this week's plenary session include legislation on "regulation-free zones" for across-the-board deregulation in designated industries. (Yonhap)