Ukrainian President Volodymyr Zelenskyy suspended all foreign state visits and pulled troops from some areas in Kharkiv where Russia continued to make battlefield progress Wednesday.
Kyiv confirmed that Russian infantry had entered the northeastern town of Vovchansk, some 5 kilometers (3 miles) from the border.
The capture would be Russia's most significant gain since it launched an incursion into the Kharkiv region Friday, opening a new front and forcing Kyiv to rush in reinforcements.
The assault keeps Ukraine's stretched and depleted forces off balance ahead of what Zelenskyy has said could be a big Russian offensive in the coming weeks. Moscow has been slowly making ground in the east for months.
"The situation is extremely difficult. The enemy is taking positions on the streets of the town of Vovchansk," Oleksiy Kharkivskiy, Vovchansk's patrol police chief, said on Facebook.
Ukrainian troops pulled back to "more advantageous" positions in two areas of the Kharkiv region, including the Vovchansk area, the military said late Tuesday.
It said the decision was "a consequence of enemy fire and storming action" and taken "to preserve the lives of our servicemen and avoid losses."
Dmytro Lazutkin, spokesperson for the Defense Ministry, said "some" Russian infantry groups had entered the town, which military analysts reckon Moscow needs to capture to continue its offensive thrust in that direction.
Kyiv's forces were trying to prevent Russia from building up troops and military hardware in Vovchansk's north, the military said. The Russians were trying to regroup and dig in and had not taken any more "active" action on Wednesday, it added.
Police remained in Vovchansk and were continuing to evacuate people, Kharkivskiy said. Nearly 8,000 people have been evacuated from Vovchansk and border areas since Friday's assault.
Zelenskyy has postponed all his foreign travel, his spokesman Sergiy Nykyforov said, after the Ukrainian leader held a daily conference call with senior military figures to discuss the situation in the Kharkiv region and the supply of weapons.
"Volodymyr Zelenskyy has instructed that all international events scheduled for the coming days be postponed and new dates coordinated," Nykyforov wrote on Facebook.
Ukraine is trying to snuff out the assault in the Kharkiv region while holding the line against Moscow's main thrust in the eastern Donbas region and guarding against potential new border incursions.
Ukraine's top military spy has warned that Russia had small groups of forces located to the north of the Kharkiv region along the Sumy region.
Kyiv says the Russian assault into the northeast does not present an imminent threat to the region's city of Kharkiv, Ukraine's second-largest, home to 1.3 million people.
Ukraine's shortage of troops is compounded by months of delayed deliveries of weapons, in particular from the United States where Congress took six months to approve a major aid package.
The deteriorating situation in the Kharkiv region coincided with a visit to Kyiv by U.S. Secretary of State Antony Blinken who said some of the U.S. aid had arrived and more was on the way. That, he said, would "make a real difference."
"I know this is a really, really difficult time. Your soldiers, your citizens, particularly in the northeast in Kharkiv, are suffering tremendously," he said.
"But they need to know, you need to know, the United States is with you, so much of the world is with you. And they’re fighting not just for a free Ukraine but for the free world, and the free world is with you too."
