The diplomatic olive branch came as the isolated regime faces increasing global pressure following its second intercontinental ballistic missile test on July 28, with the United Nations Security Council set to vote this weekend on new sanctions.
When the situation in the South China Sea becomes "generally stable and if there no major disruption from outside parties", both parties can then start their consultations in time for the ASEAN Leaders' Summit in November, the Chinese foreign minister said.
North Korea's missile testing has become a bone of contention between ASEAN and the administration of US President Donald Trump, which has been asking ASEAN members to downgrade their ties with Pyongyang.
North Korean exports of coal, iron, iron ore, lead, lead ore and seafood are banned.
Following the foreign ministers meeting is Monday's annual ASEAN Regional Forum (ARF), which gathers 27 foreign ministers - including those of Russia, Japan, South Korea, the United States, China and North Korea - to discuss Asian security issues.
Acting U.S. Assistant Secretary of State for East Asian and Pacific Affairs Susan Thornton said countries locked in the sea disputes should halt provocative moves to foster a diplomatic resolution.
Tillerson's remarks might be an attempt to try another tack by the United States, which also has tried to get Pyongyang's ally China to use its influence to prevent North Korean leader Kim Jong Un from building a nuclear arsenal. He took back the announcement later and said the communique may be made public with other statements on Tuesday.
China, North Korea's biggest trade partner, has said it is committed to fully enforcing sanctions, but that sanctions are not a lasting solution.
Several ASEAN diplomats said that among the members who pushed for a communique that retained the more contentious elements was Vietnam, which has competing claims with China over the Paracel and Spratly archipelago and has had several spats with Beijing over energy concessions.
Earlier Sunday, China Foreign Minister Wang Yi said ministers had agreed on a three-step process for the development of the Code of Conduct. It's not clear if the ministers will push for a legally binding code.
The COC is supposed to be the legally binding version of the non-binding Declaration on the Conduct of Parties in the South China Sea (DOC). China has repeatedly said that while sanctions need to be imposed, they can not bring a final resolution to the North Korea issue, which has to be addressed by talks.
Critics say the outline of key principles is lopsidedly in China's favor and suspect that Beijing may have consented to it to divert protests as it tries to complete and fortify man-made islands in the South China Sea with a missile defense system.
It also comes at a time when the United States - long seen as a crucial buffer against China's maritime assertiveness - is distracted by other issues and providing no real clarity about its security strategy in Asia, thus weakening Asean's bargaining position, Reuters reported.