North Korea says President Trump's demand that it abandon its nuclear program as a precondition to diplomatic negotiations is "preposterous," ruling out the possibility in a new statement Sunday. On Saturday, Mr. Trump addressed the possibility of negotiations with the North during an otherwise light-hearted speech at the annual Gridiron Club dinner in Washington, D.C., on Saturday night.

"Now we are talking and they, by the way, called up a couple of days ago. They said that, 'We would like to talk.' And I said, 'So would we, but you have to denuke, you have to denuke,"' Mr. Trump told attendees at the dinner, according to a pool report of his remarks. "We will be meeting and we'll see if anything positive happens."

But in a statement sent to CBS News by North Korea's permanent mission to the United Nations, the North Korean Foreign Ministry said U.S. demands that it denuclearize before any talks are "preposterous."

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"The U.S. is taking preposterous action by continuing to trumpet an insistence that it will not have dialogue unless a right condition is met and that it will keep watching if we have intention to abandon nuclear weapons and missiles and so on," the foreign ministry said.

"The U.S., that was terrified at the rapid development of our nuclear force and has continued to knock the door of dialogue, now feigns an indifference and advances this or that precondition," the ministry said, deploying the fractured English typically used in its diplomatic communications. "Not being content with it, it insists that it will have dialogue only for making the DPRK abandon nuclear weapons and persist in 'maximum pressure' until complete denuclearization is realized. This is really more than ridiculous."

DPRK refers to the Democratic People's Republic of Korea, the North's official name.

The prospect of negotiations comes during an apparent thaw in relations between North and South Korea after the Winter Olympics in Pyeongchang, which the North said on Sunday are "now opening a new chapter of reconciliation and cooperation." South Korean officials announced Sunday that South Korea's president will send a delegation to Pyongyang later this week for talks aimed at easing nuclear tensions and trying to lay the groundwork for talks between the U.S. and the North, CBS News' Pamela Falk reports.

The North Koreans said that the changing U.S. attitude on dialogue shows the North that the U.S. is not interested in resuming talks and alluded to the possible use of military force.

"We have intention to resolve issues in a diplomatic and peaceful way through dialogue and negotiation, but we will neither beg for dialogue nor evade the military option claimed by the U.S."

It added, in a veiled threat, "We have full capability and will to confront any option favored by the U.S."

Vice President Mike Pence had signaled that the U.S. is open to holding talks with North Korea following his trip to the Olympics. Pence told the Washington Post upon his return home from South Korea that during conversations with South Korea's President Moon Jae-in, the U.S. and South Korea had agreed on terms for "further engagement" with the North.

A planned meeting between North Korean officials and Pence in South Korea had been scrapped due to disagreements over terms of the talks.

Emily Tillett and Pamela Falk contributed to this report.