Summit comes before talks in Seoul on how to pay for the cost of stationing thousands of US troops in South Korea.

US President Donald Trump and his South Korean counterpart held a summit in New York on Monday to discuss plans to restart stalled nuclear talks between the United States and North Korea, before a meeting in Seoul to discuss sharing the cost of American soldiers stationed in South Korea.

Although negotiations with North Korea have stalled since a failed second summit between Trump and the North’s leader Kim Jong Un in February, the North has said it is willing to restart talks in late September. No date or location has been set.

“There’s been no nuclear testing at all,” Trump told reporters as he met South Korean President Moon Jae-in on the sidelines of the United Nations General Assembly.

“And the relationships have been very good … We want to see if we can do something. If we can, that’ll be great. And if we can’t, that’s fine, we’ll see what happens.”

Moon said he hopes working-level negotiations between the US and North Korea will be held soon in preparation for a third summit, but Trump said he would want to know the North’s position in the run-up to a third summit with Kim before agreeing to it.

“Right now, people would like to see that happen. I want to know what’s going to be coming out of it. We can know a lot before the summit takes place,” the US president said.

Military cost-sharing

North Korea’s chief nuclear negotiator, Kim Myong Gil, last week welcomed Trump’s suggestion for a “new method” in talks on Pyongyang’s nuclear weapons programmes, saying he wanted to be “optimistic” the US would present the “right calculation method”.

Last week, Trump distanced himself from a suggestion by his former national security adviser, John Bolton, for a Libyan model of denuclearisation for North Korea. Bolton was fired this month, with Trump naming Robert O’Brien as his new national security adviser.

Talks on renewing a military cost-sharing deal with the US will begin on Tuesday in Seoul, South Korea’s foreign ministry has said.

South Korea has shouldered part of the cost of stationing 28,500 US troops in the country since a 1991 pact. In March it signed a deal with the US to pay 1.04 trillion won ($870.94 million) this year – an increase of 8.2 percent on the year.

The agreement expires at the end of this year.

Trump has repeatedly urged the South to contribute more to the cost. “South Korea is a very wealthy nation,” he wrote last month on Twitter, adding, “Talks have begun to further increase payments to the United States”.