By Olena Harmash

KYIV (Reuters) - Ukraine has lost over 40% of the territory in Russia's Kursk region that it captured in a surprise incursion in August as Russian forces have mounted waves of counter-assaults, a senior Ukrainian military source said.

The source, who is on Ukraine's General Staff, said Russia had deployed 59,000 troops to the Kursk region since Kyiv's forces swept in and advanced swiftly, catching Moscow unprepared 2-1/2 years into its full-scale invasion of Ukraine.

"At most, we controlled about 1,376 square kilometres (531 square miles), now of course this territory is smaller. The enemy is increasing its counterattacks," the source said.

"Now we control approximately 800 square kilometres (309 square miles). We will hold this territory for as long as is militarily appropriate."

With the thrust into Kursk, Kyiv aimed to stem Russian attacks in eastern and northeastern Ukraine, force Russia to pull back forces gradually advancing in the east and give Kyiv extra leverage in any future peace negotiations.

But Russian forces are still advancing in Ukraine's eastern Donetsk region.

President Volodymyr Zelenskiy said he believed Russian President Vladimir Putin's main objectives were to occupy the entire Donbas, which consists of Donetsk and Luhansk regions, and oust Ukrainian troops from the Kursk region.

"For Putin, the most important thing is to push us out of the Kursk region. I am sure that he wants to push us out by January 20," Zelenskiy told media, referring to when Donald Trump will be inaugurated as U.S. president. "It is very important for him (Putin) to demonstrate that he is in control of the situation."The source at the Ukrainian General Staff source reiterated that about 11,000 North Korean troops had arrived in the Kursk region in support of Russia, but that the bulk of their forces was still finalising their training.

The Russian Defence Ministry did not immediately respond to a Reuters request for comment. Reuters could not independently verify the figures or descriptions given.

Moscow, which occupies about a fifth of Ukraine, has not confirmed or denied the presence of North Korean forces in Kursk region.

RUSSIAN ADVANCE IN EASTERN UKRAINE

The General Staff source said the Kurakhove region was the most threatening for Kyiv now as Russian forces were advancing there at 200-300 metres (yards) a day and had managed to break through in some areas.

The town of Kurakhove is a stepping stone towards the logistical hub of Pokrovsk in the Donetsk region.

Russia has about 575,000 troops fighting in Ukraine now, the source said, and aims to increase its forces to around 690,000.

Russia does not disclose numbers involved in its fighting. Reuters could not verify those figures.

Ukraine has sought to disrupt Russian logistics and supply chains by hitting Russian weapons and ammunition depots, airfields, and other military targets inside Russia.

After U.S. President Joe Biden allowed Kyiv to fire U.S.-supplied missiles at targets deep inside Russia, Ukraine last week fired U.S. ATACMS and British Storm Shadow cruise missiles into Russia.

On Thursday, Russia launched a new medium-range ballistic missile into the Ukrainian city of Dnipro, in a likely warning to NATO.

Ukrainian officials are holding talks with the United States and Britain on new air defence systems capable of protecting Ukrainian cities and civilians from the new longer-range aerial threats.

The Ukrainian General Staff source said the military had implemented measures to bolster air defences over Kyiv and planned similar steps for Sumy in the north and Kharkiv in the northeast.

(Reporting by Olena Harmash; editing by Mark Heinrich)