Donald Trump has invited Kim Jong-un to the US after becoming the first sitting American president to enter North Korea.

The apparently impromptu meeting came about after Trump tweeted an invitation to Kim on Saturday from the G20 summit in Osaka, Japan.

After shaking hands with Kim in the demilitarised zone (DMZ) between the two Koreas and walking with him over the border, Trump said: “Stepping across that line is a great honour. Great progress has been made, great friendships have been made and this has been, in particular, a great friendship.”

Following a trilateral meeting between Kim, Trump and the South Korean president, Moon Jae-in, Trump later said he agreed with Kim to restart talks after nuclear negotiations stalled earlier this year and had invited him to the US “when the time is right”.

Trump said he and Kim were “not looking for speed. We’re looking to get it right.” He added: “We are going to have teams, they are going to meet over the next weeks, they are going to start a process and we will see what happens.”

He said sanctions would remain in place, but suggested Washington might be willing to offer concessions in return for piecemeal North Korean moves towards denuclearisation – an approach it had previously rejected. “At some point during the negotiation things can happen,” he said.

Kim said the meeting at the heavily armed border, which was originally supposed to be a brief exchange of pleasantries but lasted almost an hour, was symbolic of warming ties between the US and North Korea.

“I think meeting here, two countries that have a hostile past, we are showcasing to the world that we have a new present and we have a positive meeting going forward,” he said.