North Korea's leader has expressed "great satisfaction" after receiving a letter from US President Donald Trump, the North's state media said, reports BBC.
The letter was passed to Kim Jong-un by one of his top aides, who went to Washington last week.
The two men are planning to meet for a second time by the end of February, according to the White House.
They first met last June in Singapore to discuss the possible denuclearisation of North Korea.
Little progress has been made on the issue since then, but there has been a flurry of diplomatic activity towards a second summit this month.
Kim Jong-un visited China for talks with President Xi Jinping, as he did before the Singapore summit, while his top negotiator Kim Yong-chol met President Trump at the White House.
"Kim Jong-un said that we will believe in President Trump's positive way of thinking, wait with patience and in good faith and, together with the US, advance step by step toward the goal to be reached by the two countries," North Korean state run news agency KCNA said.
The report also said Mr Kim "spoke highly of President Trump for expressing his unusual determination and will" towards a second summit.
No venue has been announced for the new talks but observers say Vietnam could be a potential location.
Mr Kim's conciliatory tone comes after the North Korean leader in his New Year speech warned his country might change course if the US continued to uphold economic sanctions against it.
Last year's rapprochement and the Singapore summit came after a turbulent 2017 marked by North Korea testing missiles that could reach the US mainland and an escalation in rhetoric with both sides trading insults and threats of nuclear destruction.
The 2017 summit ended with a general agreement towards denuclearisation but little has been achieved since.
The North has not provided a detailed account of its nuclear facilities and international sanctions remain in place.
