Oleksii Liskonih/iStock(WASHINGTON) -- North Korea has said it was willing to meet with the U.S. in late September to resume talks focused on its nuclear weapons program -- a move that President Donald Trump heralded as a "good thing" after weeks of quiet in the diplomatic process.

North Korea is willing "to sit with the U.S. side for comprehensive discussions of the issues we have so far taken up, at the time and place to be agreed late in September," said the regime's Vice Foreign Minister Choe Son Hui, according to the state-run Korean Central News Agency.

The potential offer comes nearly two months after the U.S. and North Korea were supposed to meet over the summer. After Trump and Kim Jong Un met at the Demilitarized Zone between North and South Korea in late June, his administration said working-level talks would resume by mid-July. Those would be a critical set of meetings for the U.S. to hammer out an agreement on eliminating North Korea's nuclear weapons program in exchange for United Nations sanctions relief after the two leaders failed to reach one in Hanoi, Vietnam, in February.

But for weeks now, those talks have not happened, despite Secretary of State Mike Pompeo repeatedly saying they would in a "couple of weeks."

Hopes that they could take place during the U.N. General Assembly later this month seemed dashed last week when North Korea announced its Foreign Minister Ri Yong Ho would not be attending, instead sending a lower-level delegation. With Monday's announcement, however, it seems the General Assembly in late September could be the moment after all.

"We're hopeful that in the coming days or perhaps weeks we will be back at the negotiating table with them," Pompeo told ABC News Chief Anchor George Stephanopoulos on "This Week" Sunday.

A State Department spokesperson told ABC News on Monday they don't have "any meetings to announce at this time."

But Trump welcomed North Korea's statement with optimism.

"I have a very good relationship with Chairman Kim. ... They would like to meet. We'll see what happens. I always say having meetings is a good thing, not a bad thing," he told reporters on the White House south lawn Monday afternoon.

To the North, however, the statement was a warning and an ultimatum, too, "If the U.S. side fingers again the worn-out scenario ... the DPRK-U.S. dealings may come to an end."

That appeared to be a reference to the U.S. demand in Hanoi that North Korea take steps to dismantle its nuclear weapons program before the U.N. sanctions were lifted.

Kim has rejected that sequencing, instead offering only to dismantle one key nuclear facility in exchange for all economic sanctions being lifted.

While the Trump administration says that demand has not changed, the North Korean vice foreign minister expressed optimism that "the U.S. side will come out with a proposal geared to the interests of the DPRK and the U.S. and based on the calculation method acceptable to us."

U.S. special envoy Stephen Biegun, who has been tasked with leading working-level talks but only met one-on-one with the North Koreans right before the Hanoi summit, said last Friday the U.S. still hadn't heard from the North Koreans about setting up a meeting, but reiterated that the door was open and they were ready to talk.

"We have made clear to North Korea that we are prepared to engage as soon as we hear from them. We are ready, but we cannot do this by ourselves," Biegun said at the University of Michigan.

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