UNITED NATIONS — Secretary of State Mike Pompeo visited the United Nations on Friday to deliver the message that there would be no sanctions relief for North Korea until its leader does “what he promised the world he would do” by surrendering the North’s nuclear weapons.

At a news conference after his meetings, Mr. Pompeo also said that North Korea, under its leader, Kim Jong-un, was continuing to find ways to skirt the sanctions aimed at dismantling the North’s nuclear arms program. Mr. Pompeo said he urged other members of the United Nations Security Council to “step up their enforcement efforts” on the sanctions, which he called “critical to our achieving this goal” of pressing Mr. Kim to give up his country’s nuclear weapons.

His visit to the United Nations, Mr. Pompeo’s first as secretary of state, appeared partly intended to quell speculation that the Trump administration might be willing to relax its position on the sanctions, now that President Trump and Mr. Kim have established a personal relationship through their summit meeting in Singapore last month.

Mr. Trump has said that the North Korean leader pledged at that meeting that he was prepared to denuclearize. Mr. Kim has yet to take any concrete steps in that direction, raising doubts about his intentions.