GENEVA — North Korea’s latest test of an atomic weapon leaves the United States with an uncomfortable choice: Stick with a policy of incremental sanctions that has clearly failed to stop the country’s nuclear advances, or pick among alternatives that range from the highly risky to the repugnant.

A hard embargo, in which Washington and its allies block all shipping into and out of North Korea and seek to paralyze its finances, risks confrontations that allies in Asia fear could quickly escalate into war. But restarting talks on the North’s terms would reward the defiance of its young leader, Kim Jong-un, with no guarantee that he will dismantle the nuclear program irrevocably.

Speaking in Geneva early Saturday morning after announcing a deal with Russia over the Syrian conflict, Secretary of State John Kerry said the United States was willing to negotiate with North Korea, but only if it agreed that the goal of those talks was for it to give up its weapons. “We have made overture after overture to the dictator of North Korea,” he said, including on normalizing the country’s relationship with the West and a formal peace agreement to replace the 1953 armistice that halted the Korean War but not the state of hostilities.

“All Kim Jong-un needs to do is say, ‘I’m prepared to talk about denuclearization,’” Mr. Kerry said.