It comes only a day after he officially called off the planned June 12th meeting with Kim Jong Un
Donald Trump has said his summit with Kim Jong Un could still happen next month, despite the US having called it off yesterday.
In a letter to the North Korean leader yesterday, President Trump said he was cancelling the planned June 12th summit in Singapore due to "tremendous anger and open hostility" in a recent North Korean statement.
Following the letter, North Korean officials responded by stating they were ready to talk at 'any time'.
In a statement quoted by the state KCNA news agency, First Vice Foreign Minister Kim Kye Gwan said: "We remain unchanged in our goal, and will to do everything we can for the peace and stability of the Korean peninsula and humankind.
"The first meeting would not solve all, but solving even one issue at a time in a phased way would make the relations get better rather than making them get worse. The US should ponder over it."
Speaking to reporters at the White House today, President Trump said: "We'll see what happens. It could even be the 12th. We're talking to them now.
"They very much want to do it. We'd like to do it."
When asked further about the situation and whether North Korea is playing games, he added: "Everybody plays games, you know that."
President Trump had earlier taken to Twitter to welcome the North Korean statement:
Very good news to receive the warm and productive statement from North Korea. We will soon see where it will lead, hopefully to long and enduring prosperity and peace. Only time (and talent) will tell!— Donald J. Trump (@realDonaldTrump) May 25, 2018
It came after North Korea warned of a "nuclear showdown" and described US Vice President Mike Pence "ignorant" and "stupid" over recent comments.
The North Korean regime appeared to be objecting to Mr Pence's suggestion the North may end up like Libya "if Kim Jong Un doesn't make a deal" and relinquish his country's nuclear weapons programme.
Libya's ex-leader Muammar Gaddafi was killed in an uprising years after giving up atomic weapons in exchange for the easing of sanctions - a precedent which has appeared to cause concern for North Korea.