Frustrated by the lack of sanctions relief after three summits with US President Donald Trump, North Korea has warned of a New Year's surprise if the United States does not come up with concessions by the end of the year.

At a UN Security Council session on North Korea, the US ambassador, Kelly Craft, voiced concern that the authoritarian state was indicating it would test intercontinental ballistic missiles "which are designed to attack the continental United States with nuclear weapons.

"Missile and nuclear testing will not bring the DPRK greater security," Craft said, referring to the North by its official name, the Democratic People's Republic of Korea.

"We trust that the DPRK will turn away from further hostility and threats, and instead make a bold decision to engage with us," she said.

Hinting at further sanctions, Craft said: "If events prove otherwise, we, this Security Council, must all be prepared to act accordingly."

Craft appeared to rule out meeting North Korea's demands for an offer in the year's final weeks, saying: "Let me be clear: The United States and the Security Council have a goal -- not a deadline."

But she said the United States was willing to keep talking.

"We remain ready to take actions in parallel, and to simultaneously take concrete steps towards this agreement," Craft said.

"We are prepared to be flexible in how we approach this matter."