The Trump administration pushed ahead with hopes for a summit soon with Kim Jong Un, the North Korean leader, after talks Thursday with envoys from Pyongyang and the announcement of a meeting Friday between the country’s top nuclear negotiator and President Trump.

After discussions in New York, Secretary of State Mike Pompeo said he was “confident we are moving in the right direction.’’

Pompeo maintained that the United States would continue to demand a fully verifiable and irreversible denuclearization of the Korean Peninsula. But he acknowledged that significant challenges remained and predicted more “tough moments and difficult times’’ as the two sides negotiated.

Still, Pompeo cited “real progress’’ in rescheduling a summit meeting between Kim and Trump that was set for June 12 in Singapore, before the US president canceled it last week.

It would be “nothing short of tragic to let this opportunity go to waste,’’ Pompeo told reporters after 2½ hours of discussions with Kim Yong Chol, the former North Korean intelligence chief and top nuclear arms negotiator.

“If these talks are successful, they will truly be historic,’’ he said.

The diplomacy is expected to continue Friday in Washington, where Trump is planning to receive a letter from the North Korean leader, hand-delivered by his envoys.

In remarks to reporters Thursday, Trump said it was not clear if the show of tenuous détente would be enough to strike a deal to hold the summit meeting but said negotiations between Washington and Pyongyang — which both sides hope will end decades of enmity and suspicion — are “in good hands.’’

The meeting set for Friday came as a surprise even to some on Trump’s staff and he offered few details when he announced it. It would be a rare visit similar to one made to Washington in 2000 by Vice Marshal Jo Myong Rok, who was then North Korea’s second-most-powerful official. Jo met President Bill Clinton and delivered a letter from North Korea’s leader at the time, Kim Jong Il.

Trump’s decision to personally meet the North Korean envoy displayed his eagerness to be at the center of the action for the high-stakes talks.

A senior State Department official told reporters Wednesday night that it would be natural for the North Korean delegation to pass communications through Pompeo, to then deliver to the president. The official, who spoke on condition of anonymity, said then that he would be surprised if the envoys delivered a letter to the president personally.

Michael Green, a former senior Asia adviser to President George W. Bush, said the flurry of diplomatic activity had already led South Korea, Russia, and China to either propose, consider, or undertake a softening of sanctions.

“North Korea’s goal is to defuse sanctions and it’s already working,’’ Green said. “There’s nothing that the North Koreans have put on the table that suggests any serious intent to denuclearize.’’

US and North Korean envoys have also been meeting in Panmunjom, in the Demilitarized Zone between North and South Korea, and another set of officials has held talks in Singapore to hash out the logistics of putting the June 12 summit meeting back on. The blizzard of meetings represents a breathtaking change from the bellicose language the two sides lobbed at each other for much of last year, with Trump threatening to unleash “fire and fury’’ against North Korea if it endangered the United States.

But the two sides still remain far apart. The Trump administration has largely insisted that North Korea commit itself to a rapid and complete unwinding of its nuclear program, although the president recently opened the door to a phased dismantling.

President Moon Jae-in of South Korea, who served as an early mediator between Washington and Pyongyang, is known to favor a step-by-step process that would lift some sanctions against North Korea in exchange for verifiable steps to stop or reverse its weapons programs. North Korea is thought to favor such an approach.

A senior South Korean official warned Wednesday that differences between the two sides were substantial.

“It won’t be easy to narrow the gap and find common ground, but I think it would not be impossible,’’ Cho Myoung-gyon, the South’s unification minister, said in a speech in Seoul.

Trump is not the only president of a world power seeking a meeting with the North Korean leader.

In Pyongyang on Thursday, Russian foreign minister Sergey Lavrov became the first senior Russian official to meet with Kim Jong Un. Lavrov also extended an invitation from President Vladimir Putin of Russia for Kim to visit Moscow.

Lavrov called for the lifting of sanctions on North Korea and endorsed moves toward reconciliation on the Korean Peninsula.

“It’s absolutely clear that when starting a discussion about solving the nuclear problem and other problems on the Korean Peninsula, we proceed from the fact that the decision cannot be complete while sanctions are in place,’’ Lavrov said.

It was the first visit by the Russian foreign minister to North Korea in a decade and seemed designed to reassert Moscow’s long-standing interests in the Koreas on the eve of the possible summit meeting between Kim and Trump.

Before leaving Moscow, Lavrov had said Russia was not involved in talks over the US-North Korea summit meeting. But Moscow was a party in previous negotiations on the nuclear question, and it has offered itself as a possible mediator between North and South.

In addition, Putin has made a habit of looking for gaps and weaknesses in US foreign policy that he can exploit. His spokesman, Dmitry Peskov, said it was premature to discuss the timing of any such visit by Kim to the Russian capital.

Russia shares an 11-mile border with North Korea, which earns an estimated $120 million annually by seizing the wages of construction workers employed in Russia, according to the Database Center for North Korean Human Rights, a group in Seoul.