UNITED NATIONS — Secretary of State Rex W. Tillerson said on Friday that the United States was keeping “all options” on the table if diplomacy failed to persuade North Korea to halt its nuclear weapons program.

Speaking at the United Nations Security Council, Mr. Tillerson called for stiffer international sanctions against North Korea and threatened to impose sanctions on third parties that continued to cooperate with the country. He also demanded that the North dismantle its nuclear weapons program before talks could begin.

“The more we bide our time, the sooner we will run out of it,” he said. “All options for reacting to future provocations must remain on the table.”

He added, “North Korea must take concrete steps to reduce the threat that its illegal weapons programs pose to the United States and our allies before we can consider talks.”