Ukrainian President Volodymyr Zelenskyy said Tuesday that the thousands of North Korean soldiers expected to reinforce Russian troops on the front line in Ukraine are pushing the almost three-year war beyond the borders of the warring parties.

Western leaders say North Korea has sent some 10,000 soldiers to help Russia’s military campaign and warn that its involvement in a European war could also unsettle relations in the Indo-Pacific region, including Japan and Australia.

Zelenskyy said he spoke to South Korean President Yoon Suk Yeol and told him that 3,000 North Korean soldiers are already at military bases close to the Ukrainian front line and that he expects that deployment to increase to 12,000.

At the Pentagon on Tuesday, spokesman Maj. Gen. Pat Ryder said a “relatively small number” of North Korean troops are now in Russia's Kursk region, where Russian troops have been struggling to push back a Ukrainian incursion, and a couple thousand more are heading in that direction.

South Korea, which has been in close contact with NATO, the U.S. and the European Union about the latest developments, warned last week that it could send arms to Ukraine in retaliation for the North's involvement.

“There is only one conclusion — this war is internationalized and goes beyond the borders" of Ukraine and Russia, Zelenskyy wrote on Telegram.

The Ukrainian president also said he and Yeol agreed to step up their countries' cooperation and exchange more intelligence, as well as develop concrete responses to Pyongyang's involvement.

In Washington, White House national security adviser Jake Sullivan met Tuesday with Zelenskyy's top adviser to discuss the North Korean troops as well as a coming surge of weaponry that the U.S. is delivering to Kyiv to help the Ukrainians harden protection of their energy infrastructure, according to White House officials familiar with their private talks.

Sullivan and Andriy Yermak, head of the Ukrainian president’s office, shared concerns that North Korean troops could be deployed to Russia's Kursk region and what such a development could mean for the conflict.

The officials, who were not authorized to comment publicly, said during the two-hour meeting at the White House, Sullivan also briefed Yermak on President Joe Biden’s plans to push additional artillery systems, ammunition, hundreds of armored vehicles and more to Ukraine before he leaves office in January.

Sullivan told Yermak that by year’s end, the U.S. administration plans to provide Ukraine with 500 additional Patriot and ARAAM missiles to help bolster air defenses, according to the officials.

Meanwhile, North Korea said its top diplomat is visiting Russia in another sign of their deepening relationship.

Tensions on the Korean Peninsula are at their highest point in years, with North Korea continuing a run of provocative weapons tests and South Korea and the U.S. expanding their military drills.

Russian drones, missiles and bombs smashed into Kyiv and Kharkiv, Ukraine’s biggest cities, in nighttime attacks, killing four people and wounding 15 in a continuing aerial onslaught, authorities said Tuesday.

Russia has bombarded civilian areas of Ukraine almost daily since its full-scale invasion of its neighbor, causing thousands of casualties.

The Russian army is also pushing hard against front-line defenses in the eastern Donetsk region of Ukraine. The Russian Defense Ministry claimed Tuesday that Russian troops captured the Donetsk town of Hirnyk and the villages of Katerynivka, and Bohoiavlenka.

Zelenskyy also spoke about the war at a meeting Tuesday in Reykjavik with the leaders of Denmark, Iceland, Finland, Norway and Sweden. He said a conference will begin in Canada on Wednesday to address the abduction of what he said were tens of thousands of children by Russia from Ukraine’s occupied territories.

A Russian aerial attack struck Kharkiv, in Ukraine’s northeast, at around 3 a.m., hitting a house and killing four people, regional Gov. Oleh Syniehubov said. Nearly 20 houses were damaged in the attack, he said.

Several hours earlier, Russia dropped a glide bomb on the landmark Derzhprom building in the Kharkiv city center, injuring seven people, Mayor Ihor Terekhov said. Derzhprom, also known as the Palace of Industry, is being considered for inclusion on UNESCO’s World Heritage List.

Terekhov said Russia has concentrated attacks on Kharkiv in recent days. He urged people not to ignore air raid warnings.

Authorities in Kyiv said debris from intercepted Russian drones fell on two city districts, injuring six people.

Ukraine has also used long-range drones to disrupt Russia’s war machine and embarrass the Kremlin by striking targets on Russian soil.

A special forces academy in the Russian province of Chechnya was hit by drones, causing a fire that was quickly extinguished, according to Chechen leader Ramzan Kadyrov, who is close ally of Russian President Vladimir Putin.

It was the first drone attack of the war on Chechnya, which lies about 800 kilometers (500 miles) east of Ukraine.