US President Donald Trump on Saturday backed a possible third summit with North Korea, after Kim Jong Un said he would be willing to meet his American counterpart if Washington comes to the table with the “right attitude”.

Kim said he would wait until the end of the year “for the US to make a courageous decision” to change its approach and smooth the path to another meeting, state media reported, after his most recent summit with Trump in Vietnam broke down without agreement.

Trump welcomed further talks between the pair, pointing to their “excellent relationship”.

Read: Trump floats idea of third North Korea summit

“I agree with Kim Jong Un of North Korea that our personal relationship remains very good, perhaps the term excellent would be even more accurate, and that a third Summit would be good in that we fully understand where we each stand,” he said on Twitter.

Washington has blamed the February deadlock on the North's demands for sanctions relief in return for limited nuclear disarmament, but Pyongyang said it had wanted only some of the measures eased.

And Trump has hinted that the punitive measures could eventually come to an end.

“North Korea has tremendous potential for extraordinary growth, economic success and riches under the leadership of Chairman Kim,” the American president said.

“I look forward to the day, which could be soon, when Nuclear Weapons and Sanctions can be removed, and then watching North Korea become one of the most successful nations of the World!” In a speech to Pyongyang's rubber-stamp parliament on Friday, Kim said the Hanoi meeting had made him question whether Washington is “genuinely interested” in improving its relations with Pyongyang.

“We are willing to give another try if the US offers to have a third summit with the right attitude and mutually acceptable terms,” he said, according to a report by North Korean state media outlet KCNA.

Kim added that his personal relationship with Trump remained strong, and they could “write letters to each other” whenever they wanted.

“We will wait with patience until the end of the year for the US to make a courageous decision,” Kim said.

Renewed sign of tension

Pyongyang has been careful not to criticise Trump personally, while attacking sanctions on North Korea as an attempt to “destroy modern civilisation and turn the society back in a medieval dark age”.

However, in a renewed sign of tension on the Korean peninsula, KCNA published a strongly-worded criticism of the South's deployment of the first two F-35A advanced stealth fighters.

They are part of an eventual fleet of 40 of the US jets Seoul plans by 2021.

The state news agency called the arrival of the warplanes a “serious provocation” and a setback to hopes of peace.

“The situation is a clear reminder of the South Korean authorities' diehard intent on military stand-off despite their outwardly hand-shake for reconciliation,” KCNA said. “The South Korean authorities should be aware of catastrophic consequences their thoughtless acts will bring, and exercise discretion.”

Trump and Kim held their first landmark summit in Singapore last June, where the pair signed a vaguely-worded agreement on the “denuclearisation of the Korean peninsula.”

But the failure to reach agreement at their second summit in Hanoi has raised questions over the future of the accord.

On Thursday, at the start of a meeting with his South Korean counterpart Moon Jae-in at the Oval Office, Trump said he was mulling a third summit with Kim -- a move supported by Seoul.

Moon brokered the US-North Korea talks and has been pushing for the resumption of inter-Korean economic projects, but doing so would fall foul of international sanctions imposed on Pyongyang.

“Our government will do what we can in order to maintain the current momentum for dialogue,” Moon's office said in a statement.

The day before, Kim accused Seoul of acting as an “overstepping mediator” and said the South should “speak up” for Pyongyang's interests.

On Friday, KCNA reported Kim was re-elected as chairman of the State Affairs Commission, the North's most important decision-making body, to cheers and loud applause from the delegates.