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(LONDON) -- North Korea's Foreign Minister Choe Son-hui left Pyongyang on Monday night for an official visit to Russia, North Korean state-controlled media reported, as the U.S. and NATO again denounced growing military cooperation between the two neighbors.

The Korean Central News Agency said Choe and her entourage departed Pyongyang International Airport on Monday, with Moscow's ambassador to the country Alexander Matsegora among those who saw the delegation off.

The visit "is taking place within the framework of a strategic dialogue -- following an agreement to enhance ties reached by the leaders of our countries during the June 2024 summit," a foreign ministry statement said.

Russia's state-run Tass news agency said Choe arrived in the Pacific port city of Vladivostok on Tuesday and would head to Moscow on Wednesday, citing a diplomatic source.

The visit comes as Western concerns grow about the presence of North Korea troops in Russia ahead of their expected deployment to reinforce Moscow's troops fighting Ukrainian forces in eastern Ukraine and western Russia.

President Joe Biden on Monday commented on the situation after casting his vote for next week's elections in Delaware.

"It's very dangerous, very dangerous," Biden told reporters.

Pentagon spokesperson Sabrina Singh told reporters at a Monday briefing that the U.S. believes there are now 10,000 North Korean troops in Russia, up from the American estimate of 3,000 given by National Security Council spokesperson John Kirby last week.

The troops have been sent "to train in eastern Russia" and "will probably augment Russian forces near Ukraine over the next several weeks," she said.

Singh said some of Pyongyang's troops are moving towards Russia's western Kursk region, where Ukrainian forces established a foothold in August.

"A portion of those soldiers have already moved closer to Ukraine, and we are increasingly concerned that Russia intends to use these soldiers in combat or to support combat operations against Ukrainian forces in Russia's Kursk Oblast, near the border with Ukraine," she said.

Singh -- like Kirby and Defense Secretary Lloyd Austin last week -- framed the deployment as a sign of Moscow's weakness.

"This would mark a further escalation and highlights President [Vladimir] Putin's increasing desperation, as Russia has suffered extraordinary casualties on the battlefield, and an indication that Putin may be in more trouble than people realize," she said.

"He's tin-cupping to the DPRK, Iran, because he has failed to meet those battlefield objectives," Singh added, using the acronym of the country's official name -- the Democratic People's Republic of Korea.

State Department spokesperson Matthew Miller, meanwhile, said the U.S. has raised the issue with long-time North Korea backer China, to "make clear that we are concerned about it, and that they ought to be concerned about this destabilizing action by two of its neighbors, Russia and North Korea."

"I'll let them speak for themselves, but we have been making clear to China for some time that they have an influential voice in the region," Miller added. "And they should be concerned about steps that Russia has taken to undermine stability. They should be concerned about steps that North Korea has taken to undermine stability and security."

 Ukrainian President Volodymyr Zelenskyy said on Tuesday morning he had spoken with South Korean President Yoon Seok-yeol to discuss the involvement of North Korean troops in the war.

"There is only one conclusion -- this war is internationalized and goes beyond the borders of two states," Zelenskyy wrote on Telegram. The president said he provided Yoon with "fresh data" on the deployment of 3,000 North Korean soldiers to Russian training grounds close to the front.

Zelenskyy said the North Korean force will eventually grow to 12,000 troops -- the highest estimate so far given by Ukraine, the U.S. or South Korea.

The two presidents "agreed to strengthen the exchange of intelligence and expertise" and to "develop an action strategy and a list of countermeasures in response to escalation" in collaboration with "mutual partners."

Yoon said on Monday that a South Korean delegation will visit Ukraine this week to share information about the deployment of North Korean troops to Russia and discuss further cooperation with Kyiv.

In a statement released by his office following the call with Zelenskyy, Yoon said Pyongyang is "engaging in a dangerous and unprecedented act."

Yoon said his government "would not overlook the military collusion between North Korea and Russia that threatens South Korea's security," and committed to "closely monitor the evolving battlefield situation and implement effective, gradual response measures."

"If North Korea, which has not engaged in modern warfare since the Korean War, were to acquire the experiences gained from the war in Ukraine and disseminate them to its military of over 1 million, it would pose a significant threat to South Korea’s security," he added.

The South Korean Yonhap news agency reported Tuesday that the country's National Intelligence Service told lawmakers that some of the North Korean generals and troops sent to Russia may have already moved to the front lines.

The NIS said the dispatched troops are from a special operations unit and are are known as the "storm troopers."

The North Korean soldiers are learning Russian military terms such as "location," "artillery fire," and "launch," suggesting they will be sent to the front lines, according to lawmakers briefed by intelligence officers.

The lawmakers said Russian trainers are teaching the new arrivals more than 100 Russian military terms, though Pyongyang's troops are believed to be "struggling with it," they said. "It is predicted that resolving the communication issues between North Korea and Russia will be unclear."

Seoul expects 10,900 North Korean troops to be sent to Russia by December.

ABC News' Ellie Kaufman, Matthew Seyler, Justin Gomez, Max Uzol, Joohee Cho and Joe Simonetti contributed to this report.

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