North Korean leader Kim Jong-un has invited Pope Francis to visit, even though the long-isolated country has no permanent priests.

Key points: Mr Trump says three or four locations are being considered for the meeting

Mr Trump says three or four locations are being considered for the meeting He says he has a good relationship with Mr Kim and is optimistic about progress

He says he has a good relationship with Mr Kim and is optimistic about progress Mr Kim has also sent an invitation for Pope Francis to visit Pyongyang

In a gesture designed to highlight the peace efforts of North Korea, South Korean President Moon Jae-in will deliver an invitation from Mr Kim when he meets the Holy Father next week during a trip to Europe.

Mr Moon will arrive at the Vatican on October 17 to reaffirm its support for peace on the Korean peninsula, presidential office spokesman Kim Eui-kyeom said.

"When he meets with Pope Francis, he will convey Chairman Kim's message that he will ardently welcome him if he visits Pyongyang," he said.

As North Korea and the Vatican have no diplomatic relations, Mr Kim told Mr Moon of his wish to meet the Pope during a meeting last month, the spokesman added.

But, with North Korea having strict rules about the practice of religion, it would be a surprising visit for the head of the Catholic church.

North Korea's constitution guarantees freedom of religion as long as it does not undermine the state, but beyond a handful of state-controlled places of worship, no open religious activity is allowed.

North Korea, which church officials estimated had a Catholic community of about 55,000 just before the 1950-53 Korean War, does not allow priests to be permanently stationed in the country.

Priests from the South occasionally visit, usually accompanying aid deliveries or humanitarian projects.

The invitation to a Pope is the first by a North Korean leader since Mr Kim's father, Kim Jong-il, invited Pope John Paul II in 2000, a trip that never happened.

Paolo Affatato, the Asia editor for Fides Catholic news agency, said a visit by the Pope to North Korea would "provide concrete support for the peace process" on the Korean Peninsula.

"North Korea can be seen in the framework of great attention that the Pope and Holy See are paying to East Asia," he said.

Asked about the possibility of a trip, a Vatican spokesman said: "Let's wait for the invitation to arrive."

He did not elaborate on the possible timing of a meeting, but the Pope has said he wanted to visit Japan next year.

Progress made on second Trump-Kim meeting

Sorry, this video has expired Donald Trump says second North Korea summit "won't be too far away"

Mr Kim's gesture came as US President Donald Trump said plans were being made for his second summit with the North Korean leader.

Mr Trump said "incredible" progress had been made in talks with the North Korea.

"Well it is happening and we're setting that up right now," Mr Trump told reporters at the White House after announcing the resignation of US Ambassador to the United Nations Nikki Haley.

He said Secretary of State Mike Pompeo had very good talks with Mr Kim over the weekend and that three or four locations were being considered.

"Timing won't be too far away," he said.

Mr Trump says he and Mr Kim have a very good relationship. ( AP: Evan Vucci )

Later Mr Trump said the second summit would be held after US congressional mid-term elections on November 6.

Speaking to reporters as he flew to Iowa for a political rally, Mr Trump said: "It'll be after the mid-terms. I just can't leave now."

Mr Pompeo echoed Mr Trump's comments when he briefly spoke to reporters at the White House.

"While there's still a long way to go and much work to do, we can now see a path where we will achieve (our) ultimate goal, which is the full and final verified denuclearisation of North Korea," he said.

Mr Trump and Mr Kim held a historic first summit in Singapore on June 12 at which Mr Kim pledged to work towards denuclearisation of the Korean peninsula.

However, his actions have fallen short of Washington's demands for a complete inventory of its weapons and facilities and irreversible steps to give up its nuclear arsenal, which could threaten the United States.

Still, Mr Trump was upbeat on progress made so far.

"You got no rockets flying, you have no missiles flying, you have no nuclear testing," Mr Trump said in the Oval Office.

"We've made incredible progress — beyond incredible.

"But I have agreed to meet.

"We have a very good relationship with Chairman Kim. I like him, he likes me, the relationship is good."

Mr Pompeo also said Mr Kim indicated he was ready to allow international inspectors into North Korea's Punggye-ri nuclear testing site and the Sohae missile engine test facility as soon as the United States and North Korea agreed on logistics.

Reuters