WASHINGTON — The Pentagon conducted a test of an unarmed intercontinental ballistic missile on Wednesday, with the timing expected to be of note in both North Korea, which recently tested its missile arsenal, and in China, which has been urged by the Trump administration to pressure North Korea on its nuclear program.

The test came a day after Secretary of State Rex W. Tillerson said that the United States was not seeking a regime change in North Korea and would be willing to talk to Pyongyang.

“We do not seek a collapse of the regime, we do not seek an accelerated reunification of the peninsula, we do not seek an excuse to send our military north of the 38th Parallel,” Mr. Tillerson told reporters at the State Department on Tuesday. Mr. Tillerson assured North Korea “we are not your enemy,” but added that Pyongyang “is presenting an unacceptable threat to us and we have to respond.”

“We would like to sit and have a dialogue with them,” Mr. Tillerson said.

American intelligence agencies recently said that North Korea was developing a missile that could reach the interior of the United States in about a year.