“It is time for us to do our jobs,” he said of efforts to reach a deal on denuclearization. “Let’s get this done. We are here, and you know how to reach us.”

There has been speculation that Mr. Biegun was hoping to meet with North Korean officials on the inter-Korean border this week. And his appeal on Monday was seen as an open invitation to such a meeting, but there was no immediate response from North Korea.

When Kim Jong-un met President Trump in Singapore in June 2018, the North Korean leader promised to “work toward complete denuclearization of the Korean Peninsula” in return for “new” relations and security guarantees from Washington. But their two subsequent meetings, as well as lower-level talks between the two sides, have failed to make progress on carrying out the Singapore deal.

During their meeting in Hanoi in February, Mr. Trump rejected Mr. Kim’s demand that all major United Nations sanctions be lifted in return for the dismantlement of one of the North’s key nuclear fuel production facilities, but not its nuclear warheads.

North Korea has since sounded increasingly impatient, accusing Washington of trying to stall negotiations as Mr. Trump remains preoccupied with a congressional attempt to impeach him and even reviving an old insult against the American leader, calling him a “dotard.” Mr. Trump tweeted last week that the North should not “interfere” in November’s election.

Mr. Kim is widely expected to use a meeting of his Workers’ Party’s Central Committee, scheduled for this month, and his annual New Year’s Day speech to reveal his new policy options.

On Monday, Mr. Biegun lamented that the recent North Korean statements had been “so hostile and negative and so unnecessary,” and said they reflected “neither the spirit nor the content of the discussions” both sides had recently held. In these meetings, Mr. Biegun said, his team has offered “any number of creative ways to proceed with feasible steps and flexibility.”