Donald Trump has received a letter from Kim Jong-un seeking a second meeting between the two leaders.
The White House said it was a "very warm, very positive letter", which showed North Korea had a "continued commitment to focus on denuclearisation".
Mr Trump and Kim held their first summit in Singapore in June. But late last month Mike Pompeo, the US secretary of state, cancelled a planned trip to Pyongyang with talks deadlocked.
Sarah Sanders, the White House spokeswoman, said: "The primary purpose of the letter was to schedule another meeting with the president, which we are open to, and are already in the process of coordinating."
She declined to say whether the next meeting would be held in Washington.
South Korean president president Moon Jae-in is due to visit Pyongyang next week for his third meeting with Kim this year.
On Sunday, North Korea refrained from displaying its intercontinental missiles in a massive parade through Pyongyang celebrating the country’s 70th birthday.
John Bolton, Mr Trump’s national security adviser, said: "President Trump tried to hold the door open to Kim Jong-un and his regime if they would denuclearise.
"But President Trump can’t make the North Koreans walk through the door he is holding open. They are the ones that have to take the steps to denuclearise, and that is what we are waiting for."
Mr Bolton said he believed North Korea could denuclearise in less than one year if it wanted to.