China, which warned two days ago that conflict could break out "any moment" in the Korean peninsula, did not comment on North Korea's missile test but stepped up dialogue with the Trump administration, state-run CCTV reported.
However, no details about the telephone conversation between Chinese State Councillor Yang and Tillerson were released to the media.
China has also cautioned North Korea against going for sixth nuclear test defying US warnings.
Chinese Foreign Minister Wang Yi last week said the conflict over North Korea could break out "at any moment" and warned there would be "no winner" in any war.
Intelligence agencies in South Korea and the US were attempting to extract more details about the missile, including its exact type.
Lu Chao, director of the Border Studies Institute at the Liaoning Academy of Social Sciences, said the latest test, despite its failure, could be another defiant message from Pyongyang that it will not change its tough stance in the face of US pressure even amid a growing threat of military action.
However, he said the failure showed that Pyongyang missile technology was flawed.
China would also face greater pressure from the US to take further action, including ratcheting up its sanctions against Pyongyang, he added.
Liu Ming, from the Shanghai Academy of Social Sciences, said Beijing was unlikely to take further action at this stage unless Pyongyang carried out its sixth nuclear test or long- term ballistic missile test as Beijing insisted that talks, not military action, were the only solution to the North Korean issues.
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