Fighting around the city of Kharkiv, which has seen Russia make its largest territorial gains in Ukraine in 18 months, has been described as “very difficult” but “under control” by Volodymyr Zelensky.
Ukraine’s president made the comments while speaking to military leaders in the north-eastern city on Thursday, just 18 miles (30km) from the Russian border.
Moscow launched a major ground assault across the border into the Kharkiv region last week.
The surprise move has further stretched Ukraine’s outgunned and outmanned forces.
Writing on Telegram, Mr Zelensky said Ukrainian soldiers were “inflicting significant losses on the occupier”.
He said: “However, the area remains extremely difficult. We are reinforcing our units.”
Kharkiv governor Oleg Synegubov said Ukraine was trying to “stabilise” the front line in the region and had managed to partially halt Russia’s advance.
According to analysis by news agency AFP, Moscow seized 278 sq km (107 sq miles) of Ukrainian territory between 9 and 15 May – figures it based on data from the Institute for the Study of War.
This has been the largest territorial gain by Russia in a single operation since mid-December 2022.
Russian President Vladimir Putin said on Wednesday his troops were advancing on “all fronts”.
Some military analysts say Moscow may be trying to force Ukraine to divert troops from other hot spots.
On Thursday, a top Nato commander said Russia did not have sufficient forces on the ground to make a major breakthrough in Ukraine.
“I’ve been in very close contact with our Ukrainian colleagues and I’m confident that they will hold the line,” US General Christopher Cavoli told journalists, AFP reported.
The intensification of Russian attacks on multiple fronts has underscored the acute ammunition and manpower shortages affecting the Ukrainian military.
The advances happened ahead of a rare international visit by President Putin to China, meeting President Xi Jinping.
During the visit, both leaders called for a “political solution” for what they termed the “Ukraine crisis”.