KYIV (Reuters) -President Volodymyr Zelenskiy travelled to the northeastern Ukrainian city of Kharkiv on Thursday, describing the battlefield situation in the region as "extremely difficult" but under control, as Russia tries to press its new offensive beyond the border areas.

Kyiv's military said its forces were fighting Russian troops in northern districts of the town of Vovchansk, but that the invaders had been unable to break through deeper into the border town some 45 km northeast of Kharkiv city.

The Russian push into the north of Kharkiv region has made small inroads since Friday, forcing Ukraine's depleted ranks of soldiers to try to hold the line on a new front and exploiting months of delays to Western weapons supplies.

"The direction remains extremely difficult - we are strengthening our units," Zelenskiy said after holding a meeting in the city with his top commander and senior military leaders. Zelenskiy postponed all his foreign trips on Wednesday as the battlefield situation deteriorated.

Kharkiv, Ukraine's second largest city which is now home to some 1.3 million people, has been pounded for months by airstrikes that defenders struggle to stop with depleted air defences covering a city just 30 km from the border.

Russian forces have pressed two main thrusts into the region, one of which has driven towards Vovchansk, 5 km (3 miles) from the border that, if captured, would be Moscow's most significant gain of the incursion so far.

"The enemy's plans to penetrate deeper into the town of Vovchansk and gain a foothold there were thwarted," the Ukrainian General Staff said in a statement.

Ukraine has scrambled to evacuate civilians from the town and other border areas and about 8,000 people have left their homes so far.

Ukrainian Interior Minister Ihor Klymenko said in a statement that the Russian military was taking civilians "captive" in Vovchansk's north and herding them into basements.

He accused Russian forces of killing a resident in Vovchansk who tried to escape on foot and refused to obey their orders.

Reuters was unable to immediately verify Klymenko's claims.

Describing the situation in Vovchansk as under control, the Ukrainian military said its defensive actions had forced Russian troops to reduce the tempo of their push into the north of the region.

Russia says it has taken control of 12 villages since it launched its attack. Its forces are now preparing to try to take the village of Lyptsi about 30 km north of Kharkiv, according to a Russian-installed official in Ukraine quoted by Russia's RIA state news agency.

"Our guys are already on the outskirts. Work is beginning to liberate it, aviation and artillery are working constantly, they do not stop," said Vitaly Ganchev.

(Reporting by Anastasiia Malenko and Yuliia Dysa; Writing by Tom Balmforth; Editing by Toby Chopra)