Meanwhile, South Korean President Moon Jae-in's envoy for China, Lee Hae-chan, had not met Chinese President Xi Jinping as of 0540 GMT, foreign ministry spokesman Cho June-hyuck said in a regular media briefing.
Meanwhile, the South Korean Navy revealed a USA nuclear-powered aircraft carrier group was to remain in the vicinity indefinitely, while Seoul's defense ministry warned it was ready to carry out a preemptive strike if it detected a missile threat from North Korea.
China has been infuriated by the USA deployment of the THAAD system in South Korea, saying it was a threat to its security and would do nothing to ease tensions with Pyongyang.
Speaking after the meeting with the envoy on Thursday, the Chinese foreign minister said that the two countries have experienced "unexpected setbacks" in bilateral ties this year, adding that relations are now "at a crossroads".
President Moon called the latest test a "reckless provocation".
Lee earlier told reporters in Beijing that Moon hopes to sit down with Xi on the sidelines of the G20 Summit in Germany in July as well as on August 24, which marks the 25th anniversary of bilateral relations.More news: House speaker says will send health bill to Senate in weeks
According to the official Xinhua news agency, Xi told Lee: "China is willing to strengthen communication with the new South Korean government".
The United States, which has 28,500 troops in South Korea to guard against the North Korean threat, has called on China to do more to rein in its ally and neighbor.
The installation of the Thaad has resulted in an unofficial boycott of South Korean companies operating in China, including the supermarket chain Lotte, which had provided land in South Korea for the deployment. Xi, in his turn, invited Moon to visit Beijing.
The ROK-China relationship is significant for peace and prosperity on the Korean Peninsula as well as Northeast Asia, Lee said, stressing that the ROK is willing to enhance pragmatic cooperation with China and push forward the bilateral strategic partnership of cooperation.
Thaad has been put into operation in the South Korean territory in case of a potential attack by North Korea, amid a recent escalation of tensions in the peninsula. "It should not hope to have it both ways".