WASHINGTON — In some of the most conciliatory remarks to North Korea made by the Trump administration, Secretary of State Rex W. Tillerson complimented the government in Pyongyang for going more than two weeks without shooting any missiles or blowing up any nuclear bombs.

“I’m pleased to see that the regime in Pyongyang has certainly demonstrated some level of restraint,” Mr. Tillerson said, suggesting that the brief pause in testing may be enough to meet the administration’s preconditions for talks.

“We hope that this is the beginning of the signal we’ve been looking for,” he said, adding that “perhaps we’re seeing our pathway to sometime in the near future of having some dialogue. We need to see more on their part. But I want to acknowledge the steps they’ve taken so far.”

That was the carrot. As for the stick, the Trump administration announced new sanctions against China and Russia on Tuesday as part of its campaign to pressure North Korea to stop its development of nuclear weapons and missiles.