Kharkiv region governor Oleh Sinegubov said on the Telegram messaging service that Ukrainian troops defending Kharkiv had reached the state border with Russia.
It was not immediately clear how many troops had reached the Russian border and where, and air raid sirens were still being sounded in Kharkiv early on Monday.
His report was echoed by Illia Ponomarenko, defence reporter with The Kyiv Independent who tweeted: “Alright, people, we have the first Ukrainian unit coming up to the Russian border as part of the counter offensive action northeast of Kharkiv.”
Olexander Scherba, Ukraine’s Ambassador to Austria until last year, tweeted a video clip which appeared to show Ukrainian forces having advanced to the border with Russia.
It messaged: ““Mr. President, we reached Ukraine’s state border with the enemy state. Mr. President, we made it!”
“Mr. President, we reached Ukraine’s state border with the enemy state. Mr. President, we made it!”
Glory to #Ukraine! Glory to Heroes!#StandWithUkraine️ #UkraineWillWin #RussiaUkraineWar
— olexander scherba🇺🇦 (@olex_scherba) May 15, 2022
Ukraine counter-attacked Russian forces on the eastern front on Monday with fighting reported near Kharkiv, after Western military agencies said Mr Putin's offensive in the Donbas region had stalled.
Ukrainian interior ministry adviser Vadym Denisenko said in televised comments that fighting near Kharkiv was "our counter-offensive".
"It can no longer be stopped ... Thanks to this, we can go to the rear of the Russian group of forces," he claimed.
The governor of the Luhansk region in the Donbas, Serhiy Gaidai, said the situation "remains difficult", with Russian forces trying to capture the town of Sieverodonetsk.
He said leaders of the Lugansk People's Republic, the territory in Luhansk controlled by Russian-backed separatists, declared a general mobilisation, adding it was "either fight or get shot, there is no other choice".
In the south, fighting was raging around the city of Kherson and Russian missiles struck residential areas of Mykolayiv, the presidential office in Kyiv said.
Nato Secretary-General Jens Stoltenberg said on Sunday that Russia's offensive in Donbas had stalled and Ukraine could win the war, an outcome few military analysts predicted when Russia invaded Ukraine on February 24.
Since then, Russian troops have taken heavy losses while blasting cities and towns to rubble, killing thousands and sending more than six million refugees fleeing into neighbouring countries. Russia denies targeting civilians.
Despite Mr Putin’s armed forces losing at least 15,000 troops, Ukrainian political and military chiefs were braced for fresh Russian offensives on Monday.
“We are preparing for new attempts by Russia to attack in Donbas, to somehow intensify its movement in the south of Ukraine,” Volodymyr Zelensky, the country’s president, said in his nightly address.
He also stressed: “The occupiers still do not want to admit that they are in a dead-end and their so-called ‘special operation’ has already gone bankrupt.”
Ukraine’s Joint Forces Task Force said its troops had repelled 17 attacks on Sunday and destroyed 11 pieces of Russian equipment.
The command of Ukraine’s air force said Ukrainian forces downed two helicopters, two cruise missiles, and seven drones. .
Russia continued to target civilian areas along the entire front line in the Luhansk and Donetsk regions, firing at 23 villages and towns, the task force added, though all its claims could not be independently verified.
If Ukraine can sustain pressure on Izium and Russian supply lines, it will be harder for Moscow to encircle Ukrainian troops in the Donbas, who are well dug in and well trained.
Ukraine’s military also acknowledged setbacks, saying Russian forces “continue to advance” in several areas in the Donbas region.
In western Ukraine near Poland, missiles also destroyed military infrastructure overnight on Saturday and were fired at the Lviv region from the Black Sea, Ukrainian officials said.
Another ten civilians were wounded in the southern region of Mykolaiv, the regional council said, without providing details.
Mr Putin has largely refocused his military campaign on the Donbas region, which includes the Donetsk and Luhansk areas held by Moscow-backed separatists, after the failure of his initial invasion plan which included seizing Kyiv within days.
While his forces are making some gains in the Donbas region, they are also losing territory in other areas, and their advances are believed to be significantly slower than planned.
There was also no let-up on Sunday in Russia’s bombardment of the steelworks in the besieged southern port of Mariupol, where hundreds of Ukrainian fighters are holding out weeks after the city fell into Russian hands, the Ukrainian military said.
Brightly burning munitions were shown cascading down on the steel works in a video posted by a pro-Russian separatist commander.
Mr Zelensky said “very difficult and delicate negotiations” were going on to try to save Ukrainians in Mariupol and Azovstal.
In the port city, some residents ate and talked outside their burnt out apartment building, which was shelled and caught fire in early April.
“I was in the kitchen when the smoke appeared,” one resident named Natalya said. “I started carrying out my belongings, saving what I could.”
She said three neighbours had died in the fighting.
“We could not bury them because of the shelling. Each day we’ve been putting a person into a grave, but we could not cover it up with soil because of the shelling.”
To the north of Ukraine, Mr Putin’s key ally President Alexander Lukashenko has ordered Belarus’ special operations forces to deploy along the border with Ukraine to try to stop it redeploying troops to the Donbas, British defence chiefs said on Monday.
They believe Lukashenko, dubbed “Europe’s last dictator”, is seeking to play a “balancing” game of supporting the Russian president’s invasion of Ukraine while also avoiding his economy being hit by western sanctions.
They stressed that while Belarusian forces had not taken part in the invasion, its territory had been used to launch Russian air and missile strikes.
In its latest intelligence update, the Ministry of Defence in London said: “Following exercise activity earlier this month, Belarus has announced the deployment of special operations forces along the Ukraine border, as well as air defence, artillery and missile units to training ranges in the west of the country.
“The presence of Belarusian forces near the border will likely fix Ukrainian troops, so they cannot deploy in support of operations in the Donbas.”
It added: “Despite early speculation, to date Belarusian forces have not been directly involved in the conflict.
“However, Belarusian territory was used as a staging post for Russia’s initial advance on Kyiv and Chernihiv. Russia has also launched air sorties and missile strikes from Belarus.
“Belarusian President Lukashenko is likely balancing support for Russia’s invasion with a desire to avoid direct military participation with the risk of Western sanctions, Ukrainian retaliation and possible dissatisfaction in the Belarusian military.”