Speaking to reporters after meeting Pompeo on the sidelines of a regional summit in Singapore, Chinese State Councillor Wang Yi said Pompeo told him he was "was willing to maintain constructive contact".
At a news conference later, Wang said: "We believe that without any disturbances from the outside, COC consultations will accelerate".
Meanwhile the USA - traditionally the dominant military power in the area - has more frequently carried out patrols aimed at ensuring freedom of navigation. Wang said the planned naval exercises in China and the computer-simulated drills in Singapore were a starting point in efforts to elevate Beijing's security relations with Southeast Asia.
Southeast Asia and China have agreed on a working text to continue long, drawn-out negotiations over a code of conduct in the disputed South China Sea, with officials from both sides on Thursday lauding it as a "milestone".
China has overlapping territorial and maritime claims in the South China Sea with several Asean members, including Brunei, Malaysia, the Philippines and Vietnam.
Singapore's Prime Minister Lee Hsien Loong and ASEAN foreign ministers pose for a group photo during the opening ceremony of the 51st ASEAN Foreign Ministers' Meeting in Singapore August 2, 2018.
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The ministers "took note of the concerns expressed by some countries on the land reclamations in the area, which have eroded trust and confidence, increased tensions, and may undermine peace, security, and stability in the region", the draft communique said, without naming China and reflecting the internal divisions over the touchy issue.
ASEAN members Cambodia and Laos, which are known China allies, have opposed the use of strong language against Beijing over the disputes.
However, it was too early to say when negotiations would be complete, he added.
Tensions have mounted in recent years as China has built up artificial islands in the waters capable of hosting military bases, and the U.S. has thrown its support behind Southeast Asian states whose maritime claims overlap Beijing's.
The minister said Asean and China also agreed on the key modalities for future rounds of COC negotiations. For years they have been discussing a pact to prevent an escalation of disputes.
"There will be the inevitable differences, if not tensions, within ASEAN on what should be in the document". You have claimant and non-claimant states.
The ASEAN ministers also welcomed rapprochement between North Korea and South Korea and the US and reaffirmed their commitment "to combat the scourge of violent extremism, radicalization and terrorism".