SEOUL (Yonhap) – South Korean Foreign Minister Yun Byung-se and U.S. Secretary of State John Kerry on Sunday discussed "specific ways" to enact a strong punishment against North Korea for its recent nuclear test, Yun's ministry said.

They spoke on the phone for about 20 minutes, as Kerry plans to visit Beijing later this week.

Yun and Kerry "discussed specific ways to push for the strongest and most comprehensive sanctions on North Korea at the U.N. Security Council" to make it pay a price for the provocation, said the ministry.

They also agreed to seek various types of "creative" cooperation for the denuclearization of the North, including five-way talks, it said.

Last week, President Park Geun-hye proposed a five-way meeting without the North, questioning the viability of the six-party negotiations also involving China, Japan and Russia.

The six-way talks have been stalled since December 2008.

The Yun-Kerry phone conversation came as the secretary is scheduled to make a two-day trip to the Chinese capital from Wednesday.

China's cooperation is essential in adopting and implementing a U.N. resolution imposing tough sanctions on Pyongyang.