The White House, however, did not identify a location for the second setting between the two leaders.
The announcement came after Trump met with North Korean envoy, Kim Yong Chol, on Friday for a discussion that included talk about Kim Jong-un's unfulfilled pledge to dismantle his country's nuclear weapons programmes.
President Trump sat down with Kim Yong Chol, a high-level official in North Korea's Communist government, in the Oval Office, White House Press Secretary Sarah Sanders said.
"President Donald J Trump met with Kim Yong Chol for an hour and half, to discuss denuclearization and a second summit, which will take place near the end of February.
"The president looks forward to meeting with Chairman Kim at a place to be announced at a later date. she said in a statement.
The press secretary told reporters: "We continue to make progress, we continue to have conversations."
The US is going to continue to keep "pressure and sanctions" on North Korea until "we see fully and verifiable denuclearization", she said.
"We had very good steps and very good faith from the North Koreans with the release of hostages and other moves and so we'll continue this conversation.And the President looks forward to it next February," Sanders' told reporters.
The North Korean envoy arrived at the White House after a closed-door meeting with Secretary of State Mike Pompeo and US special envoy for North Korea Stephen Biegun at a hotel here.
Following the White House meeting the North Korean official was invited to lunch by Pompeo.
Last year in Singapore, Trump had described his first-ever historic meeting with Kim Jong-un as "really fantastic" and said they had agreed to "sign" an unspecified document after their "very positive" summit, aimed at normalising ties and complete denuclearisation of the Korean peninsula.
The US president had said he believed he and Kim Jong-un will "solve a big problem, a big dilemma" and that by working together, "we will get it taken care of".
The summit at Singapore's Sentosa island - the first between a sitting US president and a North Korean leader - had marked a turnaround of relations between Trump, 72, and Kim, 36, after a long-running exchange of threats and insults.
The US insists it will accept nothing less than complete denuclearisation of the Korean peninsula.
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