Trump keen to meet Kim after 'successful' China talks
US President Donald Trump has said he is keen to meet Kim Jong-un after being told the North Korean leader's trip to China "went very well".
But Mr Trump said maximum sanctions and pressure on North Korea would continue ahead of proposed talks in May.
He added that denuclearisation of the Korean peninsula was now a possibility.
The comments follow Mr Kim's meeting with China's President Xi Jinping, in his first known foreign trip since taking office in 2011.
Mr Kim and his wife were greeted with a banquet and a guard of honour, with the North Korean leader reportedly saying he was committed to denuclearisation. China is North Korea's main economic ally.
On Wednesday, Mr Trump welcomed news of progress following the talks between the two leaders in Beijing after days of speculation.
"Now there is a good chance that Kim Jong-un will do what is right for his people and for humanity," Mr Trump posted, adding in the next tweet that Mr Kim also "looks forward to his meeting with me".
So is a Trump-Kim meeting going ahead?
Mr Trump's agreement to hold an unprecedented summit with Mr Kim astonished many observers.
The announcement, which would make Mr Trump the first sitting US president to meet a North Korean leader, came after months of hostility and a string of North Korean missile tests.
An initial statement from the South Korean delegation said a meeting had been agreed and would take place by May - but no place or date has officially been set.
News of the major breakthrough in tensions was met with concern in the US, with reports that Mr Trump had made the decision without consulting key figures in his administration.
However Mr Trump later tweeted that a deal with North Korea was "very much in the making".
But despite the progress in recent months, a number of factors could affect the chances of success.
While Mr Kim has reportedly told China and South Korea he is willing to abandon nuclear weapons, he has stated that this comes with conditions, China's Xinhua news agency reported.
There are also troubling reports from North Korea.
Satellite images from last month, published by the New York Times, show what looks like a new nuclear reactor ready to go online. The newspaper claims it could produce 20kg of weapons-grade plutonium each year.
Meanwhile, US and South Korean troops are gearing up for annual military drills which the North has historically seen as provocation. They start on Monday.
Analysis by Tara McKelvey, White House reporter, BBC News
Mr Trump is planning for a win: successful negotiations with Mr Kim over his nuclear programme.
Behind the scenes, White House Chief of Staff John Kelly and others are trying to exude confidence about what they will be able to achieve at the summit. In a candid conversation with me and other visitors to his office recently, Mr Kelly described their high expectations for the meeting and their hopes for the future.
Meanwhile, the CIA director is visiting the Pentagon to discuss the matter, and US Defence Secretary Jim Mattis is coming up with contingency plans.
Details for the summit are still being worked out: the president likes to keep people guessing about how he'll negotiate and where his red lines are, and his meeting with Mr Kim is no exception.
Mr Kelly and the other aides have several weeks - or perhaps a bit longer if it's delayed - to finalise things. As they're keenly aware, the countdown has begun.
What did Mr Kim and Mr Xi discuss in Beijing?
Mr Kim arrived with his wife, Ri Sol-ju, by train on Sunday and left Beijing on Tuesday afternoon, according to reports.
The North Korean leader said the "issue of denuclearisation of the Korean Peninsula can be resolved" if the US and South Korea respond "with goodwill", Xinhua reported.
- Why Xi's the one Kim still needs to see
- Reading the moves - what our correspondents make of the visit
The North's conditions include the removal of a US nuclear guarantee for South Korea, observers say.
North Korea's KCNA news agency called the visit "a milestone" in improving bilateral ties.
Mr Kim's arrival and departure were shrouded in secrecy. China said the visit was "unofficial" - so there was no announcement of it in advance, prompting speculation about who was on the train when it was spotted arriving.
Why is Kim's visit significant?
It is the latest in a flurry of diplomatic activity since the start of the year sparked by the Winter Olympics in South Korea.
Relations between North Korea and China, historically strong, had been deteriorating, with China backing US moves to tighten international sanctions in response to the North's growing nuclear threat.
But China, a military giant over the border, is still responsible for virtually all of North Korea's food and fuel aid.
It has largely been an observer of the recent diplomatic moves by Pyongyang towards the US and South Korea.