NEW YORK — The Trump administration is willing to bargain directly with North Korea over ending its nuclear weapons program, Secretary of State Rex Tillerson said Thursday, an apparent shift in policy aimed at strengthening international resolve against what the Trump administration considers a growing menace.

Also Thursday, Bloomberg reported according to an interview with Reuters, President Donald Trump said, “There is a chance that we could end up having a major, major conflict with North Korea. Absolutely.” He added: “We’d love to solve things diplomatically, but it’s very difficult.

“Obviously, that will be the way we would like to solve this,” Tillerson said in an interview with NPR to air Friday, when the United States is convening an unusual high-level meeting at the United Nations devoted to the threat posed by North Korea’s nuclear weapons arsenal.

“But North Korea has to decide they’re ready to talk to us about the right agenda, and the right agenda is not simply stopping where they are for a few more months or a few more years and then resuming things. That’s been the agenda for the last 20 years.”

It is not fully clear what that means, but in the NPR interview and another on Thursday with Fox News, Tillerson began to sketch a diplomatic approach for the new administration that focuses on international pressure and leveraging China’s economic power over its ally.

The U.N. Security Council session Friday comes at a particularly tense time in relations between North Korea and the United States, with the Trump administration sending warships to the region in a show of force against Kim Jong Un’s regime.

This week, North Korea conducted large-scale artillery drills, showing off conventional weaponry that can easily reach South Korea’s capital, Seoul, the center of a region that is home to about 25 million people.

The Trump administration has said that military action to head off further North Korean nuclear weapons development is not out of the question, but it remains unlikely. A goal of future U.N. diplomacy could be to draw lines for when escalation by North Korea would justify retaliatory action by the United States or others, diplomats and arms control experts said.

At issue is the simultaneous effort in North Korea to perfect a nuclear warhead that could be delivered far from its shores and to develop missiles with a range long enough to be a threat to the United States.