After a morning of talks with Kim's right-hand man in New York, Secretary of State Mike Pompeo said it was not yet clear whether Pyongyang would accept nuclear disarmament.

But he claimed "real progress" had been made towards agreement on holding the summit, originally planned for June 12 in Singapore, and said Washington believes Kim is bold enough to take this step.

"It will take bold leadership from Chairman Kim Jong Un if we were able to seize this once in a lifetime opportunity to change the course for the world," Pompeo said, after his talks with Kim's number two Kim Yong Chol.

"President Trump and I believe Chairman Kim is the kind of leader who can make those kind of decisions, and in the coming weeks and months, we will have the opportunity to test whether or not this is the case."

Kim Yong Chol -- the most senior official from Pyongyang to visit the United States in 18 years -- is now expected to head to Washington to present an eagerly expectant Trump with a letter from his young leader.

But Pompeo warned that this message in itself may not be conclusive.

"This is a difficult, difficult challenge. Make no mistake about it. There remains a great deal of work to do," Pompeo said, citing ongoing talks in Singapore and in the demilitarized zone on the Korean border.

But he said that, after what has now been two meetings with Kim Jong Un and three with Kim Yong Chol, he believes the North is at least ready to consider meeting US demands for denuclearization.

US officials now expect the summit to go ahead, but they want North Korea to accept that nuclear disarmament be at the heart of the discussion -- and warn that there can be no end to trade sanctions without it.

"I believe they are contemplating a path forward. They can make a strategic shift. One that their country has not been prepared to make before. This will obviously be their decision," he said.

- Planning team -

Asked whether the answer would come on Friday, when Trump receives Kim's letter, Pompeo admitted he did not know, but added "we have made real progress in the last 72 hours toward setting the conditions."

"The conditions are putting President Trump and Chairman Kim Jong Un in a place where we think there could be real progress made by the two of them meeting," he said.

Earlier, in Washington, Trump had said he was "looking forward" to reading the letter.

Washington has demanded that the North agree to a "complete, verifiable and irreversible" end to its nuclear program, which is close to the point where it could threaten US cities with missile strikes.

Pyongyang is seeking international recognition and security guarantees and it is far from clear whether its own vision of the "denuclearization" of the Korean peninsula can be brought in line with Washington's.

Nevertheless -- after a wobble earlier this month when Trump briefly cancelled the planned summit, talks are ongoing in New York, Singapore and the DMZ.

- Russia urges caution -

Meanwhile, Russia's foreign minister visited Pyongyang on Thursday for talks with Kim Jong Un and warned against setting expectations too high, urging all sides to "avoid the temptation to demand everything and now."

Lavrov passed on greetings from President Vladimir Putin to Kim and invited him to visit Russia, the Russian foreign ministry said.

Russia is the latest major nation to reach out to North Korea since Trump accepted Kim's proposal for a summit. Kim has already had two meetings each with Chinese leader Xi Jinping and South Korean President Moon Jae-in.