SEOUL, Oct 23 (Reuters) - The United States said for the first time on Wednesday that it had seen evidence that North Korea has sent 3,000 troops to Russia for possible deployment in Ukraine, a move that could mark a significant escalation in Russia's war against its neighbor.

U.S. Defense Secretary Lloyd Austin, speaking in Rome, said it would be "very, very serious" if the North Koreans were preparing to fight alongside Russia in Ukraine, as Kyiv has alleged. But he said it remained to be seen what they would be doing there.

"There is evidence that there are DPRK troops in Russia," Austin told reporters, using North Korea's formal name, the Democratic People's Republic of Korea.

Speaking to reporters later on Wednesday White House spokesperson John Kirby said the United States believes at least 3,000 North Korean troops are undergoing training at three military bases in eastern Russia.

The U.S. determined the North Korean soldiers were transported by ship in early-to-mid October from North Korea's Wonsan region to the eastern Russian city of Vladivostok before being taken to three military training sites in eastern Russia, said Kirby.

"If they do deploy to fight against Ukraine, they're fair game," he said. "They're fair targets and the Ukrainian military will defend themselves against North Korean soldiers the same way they're defending themselves against Russian soldiers."

In Seoul, South Korean lawmakers said that Pyongyang had promised to provide a total of about 10,000 troops, whose deployment was expected to be completed by December, the lawmakers told reporters after being briefed by South Korea's national intelligence agency.

"Signs of troops being trained inside North Korea were detected in September and October," Park Sun-won, a member of a parliamentary intelligence committee, said after the briefing.

The Ukraine conflict broke out when Russia invaded its neighbor in February 2022 and has since developed into a war of attrition largely fought along front lines in eastern Ukraine, with huge numbers of casualties on both sides.

The United States said the alleged North Korean deployment could be further evidence that the Russian military was having problems with manpower.

The Kremlin has previously dismissed Seoul's claims about the North's troop deployment as "fake news" and a North Korean representative to the United Nations in New York called it "groundless rumors" at a meeting on Monday.

Both Moscow and Pyongyang have also denied weapons transfers, but they have pledged to boost military ties and signed a mutual defense treaty at a summit in June. The latest numbers came after Seoul's National Intelligence Service said on Friday the North had sent some 1,500 special forces personnel to Russia by ship and they were likely to be deployed for combat in the war in Ukraine after training and acclimatization.

Ukrainian President Volodymyr Zelenskiy has also accused Pyongyang of preparing to send 10,000 soldiers to Russia. On Tuesday he called on his allies to respond to evidence of North Korean involvement in Russia's war.

NATO allies are consulting on the North Korean deployment to Russia, a NATO spokesperson said. A Biden administration official said Moscow might send the North Koreans to eastern Ukraine or to its own Kursk region, where Russian troops have been fighting to dislodge Ukrainian forces holding a chunk of territory that they seized in an incursion that began in August.

Mike Turner, the chair of the U.S. House of Representatives intelligence committee, said in a statement that U.S. President Joe Biden should allow Kyiv to respond with U.S.-supplied arms if North Korean troops “attack Ukraine from Russian territory.”

“If North Korean troops were to invade Ukraine’s sovereign territory, the United States needs to seriously consider taking direct military action against the North Korean troops,” Turner added.