The news on Kyiv's fightback came as Russia's security service (FSB) claimed it had foiled an assassination attempt on the head of Crimea, a southern peninsula annexed by Russia in 2014.
Ukraine's troops, which have faced intense resistance in their counteroffensive launched last month, have urged Western allies to send more military support.
"Last week was difficult on the front line. But we are making progress," Ukrainian President Volodymyr Zelensky said. "We are moving forward, step by step!"
Deputy Defence Minister Ganna Malyar noted that Ukrainian forces over the past week recaptured nine square kilometres (four square miles) in the east and 28 square kilometres in the south.
Ukraine's forces have taken back over 158 square kilometres in the south since the start of the counteroffensive, Malyar said.
Russian forces are also on the offensive, and in recent days launched new assaults towards Svatove, in the eastern Lugansk region.
- Offensive extremely difficult -
Kyiv's troops have come up against heavily entrenched Russian defensive positions both along the southern and eastern fronts.
Malyar said Ukrainian troops were fighting "fierce" battles around the eastern flashpoint city of Bakhmut.
Ukraine's counteroffensive is an extremely difficult operation and it is "not a surprise" that it is not progressing at speed, a top NATO commander Admiral Rob Bauer said Monday.
"Ukraine did not reach its goals in any of the sectors," Russian Defence Minister Sergei Shoigu said, claiming that nearly all Leopard tanks provided by Poland and Portugal had been destroyed.
Shoigu and the conventional army faced a serious challenge last month when the head of the Wagner mercenary group led his forces in a rebellion against Moscow's top military brass.
In his first comments addressing the short-lived mutiny, Shoigu said Monday the rebellion "did not affect the operations of the troops."
"The plans failed primarily because the personnel of the armed forces showed loyalty to their oath and military duty," he said.
- 'Get rid' of threat -
Following the rebellion, the Kremlin gave Wagner fighters the choice of signing contracts with the Russian defence ministry, returning to civilian life or going into exile in Moscow-allied Belarus.
Russia however said there was no need for further mobilisation to replace the Wagner troops that left the battlefield.
Kyiv is fighting to try to recapture its territories in the east and south, including the Crimea peninsula, annexed by Russia in 2014.
In Crimea, the Russian security service (FSB) said Monday it had foiled an attempt on the life of the Moscow-installed head of Crimea, Sergei Aksyonov.
The FSB said it had detained a suspect -- "a Russian national born in 1988 who had been recruited by officers of Ukraine's Security Service (SBU)".
It added that the suspect was held while "removing the explosive device from its hiding place".
- 'A lot of people die' -
Moscow annexed Crimea from Ukraine after a referendum widely regarded as a sham by Kyiv and Western countries.
Increased attacks on Russian-occupied territories preceded the highly-expected fightback, which Ukraine launched last month after accumulating Western-made weapons.
Ukrainian officials have expressed frustration at the slow deliveries of weapons promised by the West.
Ukraine's military commander-in-chief Valery Zaluzhny told the Washington Post it "pisses me off" that some in the West complain about the slow start and progress to the long-awaited push against Russian occupying forces.
He also complained he has a fraction of the artillery shells that Russia is firing.
"A lot of people die every day -- a lot. Just because no decision has been made yet," Zaluzhny said.
A drone attack on a residential building in Sumy, eastern Ukraine, killed two and wounded 19, the regional administration said Monday.
Late Sunday freedom of expression group PEN also said a Ukranian writer wounded in a Russian missile strike on a restaurant last week had died.
Victoria Amelina, 37, was injured when a Russian missile destroyed the Ria Pizza restaurant in the eastern city of Kramatorsk on Tuesday, killing 12 people, including children, and wounding dozens.
In the first step towards a possible tribunal for Moscow's leadership, an international office to investigate Russia over its invasion of Ukraine opened on Monday in The Hague.