Donald Trump has said he is likely to meet Kim Jong-un in January or February and that three sites for their second meeting are under consideration.

Trump added that at some point he would invite the North Korean ruler to the United States. “We’re getting along very well. We have a good relationship,” Trump told reporters aboard Air Force One on his return from a G20 summit in Argentina.

The two sides had reportedly been engaged in talks on the leaders’ second meeting after the first, unprecedented one in Singapore in June.

The White House said in a statement on Saturday after Trump’s meeting with the Chinese president, Xi Jinping, that they and Kim would strive “to see a nuclear free Korean Peninsula”. The statement said Xi and Trump “agreed that great progress has been made with respect to North Korea”.

In November the vice-president, Mike Pence, said Trump would push for a concrete plan outlining Pyongyang’s moves to end its arms programmes. Pence told NBC News the United States would not require Pyongyang to provide a complete list of nuclear weapons and locations before the second summit, but that the meeting must produce a concrete plan.

“I think it will be absolutely imperative in this next summit that we come away with a plan for identifying all of the weapons in question, identifying all the development sites, allowing for inspections of the sites and the plan for dismantling nuclear weapons,” Pence said in November. It was essential that international sanctions pressure be maintained on North Korea until its complete denuclearisation was achieved, he said.

North Korea was angered by Washington’s refusal to ease sanctions and warned it could resume its nuclear programme.

A US thinktank said in November it had identified at least 13 of an estimated 20 active undeclared missile bases inside North Korea, underscoring the challenge for American negotiators hoping to persuade Kim to give up his weapons programmes.

North Korea entered into agreements with regional powers in 1994 and in 2005 to dismantle its nuclear programme in return for economic benefits and diplomatic rewards, but those deals broke down after Pyongyang clandestinely continued to pursue building weapons of mass destruction.