“And we’re trying to convey to the North Koreans: We are not your enemy, we are not your threat,” he said. “But you are presenting an unacceptable threat to us, and we have to respond.”

That was a somewhat different tone than the one Mr. Tillerson took when he visited Seoul in March and appeared to make North Korea’s surrender of nuclear weapons a prerequisite for talks. At that time, he said that negotiations could “only be achieved by denuclearizing, giving up their weapons of mass destruction,” and that “only then will we be prepared to engage them in talks.”

The idea that North Korea would give up its weapons at the opening of talks was dismissed immediately by allies as unworkable, and Mr. Tillerson may have simply phrased it badly. But the question now, after a series of successful missile tests, is whether Mr. Kim will decide it is time to negotiate a “freeze” on further detonations and launches — or whether he should just keep going on his current path.

Even Mr. Tillerson has, in the past, cast doubt on the wisdom of entering a “freeze,” since it would essentially enshrine North Korea as a de facto nuclear weapons state — to which a series of American presidents have said they would never agree.

Mr. Tillerson’s new position is that negotiations should begin without conditions, as long as they are ultimately headed toward denuclearization. “We don’t think having a dialogue where the North Koreans come to the table assuming they’re going to maintain their nuclear weapons is productive,” he said on Tuesday. “So that’s really what the objective that we are about is.”

Outside experts had their doubts about whether the North would take up Mr. Tillerson’s offer.

Christopher R. Hill, a former American ambassador to Seoul who led Bush-era negotiations on ending North Korea’s nuclear program, said on Saturday that Pyongyang believed the United States was cornered into accepting it as a nuclear weapons state. “We are left in a situation where they believe we will ultimately acquiesce,” he said at the KentPresents ideas festival in Kent, Conn.

At the same conference, Kathleen Stephens, another former American ambassador to Seoul, said in the case of China, India and Pakistan, “we have never succeeded in stopping a nuclear aspirant country.” She also said the North’s drive for a weapon was based on a bet that the United States could not stop it.