Kyiv launched its bid to wrest back territory controlled by Moscow in June, after stockpiling Western-supplied weapons and recruiting assault battalions.
Its efforts have focused on the war-battered town of Bakhmut in the eastern Donetsk region, as well as several points along the frontline in the south, towards Crimea.
"Two square kilometres (0.77 square miles) were liberated in the Bakhmut sector," outgoing Deputy Defence Minister Ganna Malyar said on state media.
Her announcement came one day after Kyiv said its forces had retaken Klishchiivka, a village south of Bakhmut, which was captured by Russian forces in May after one of the longest and bloodiest battles of the war.
Malyar also said Ukrainian forces had clawed back 5.2 square kilometres in the south, where its forces are working to push deeper at two points along the front.
But Ukraine's progress against entrenched Russian positions has been limited since June, spurring debate among Kyiv's Western allies over its military strategy.
Russian forces have pursued their aerial bombardment campaign, targeting Ukraine's southern regions and maritime export hubs in particular.
Ukraine said its air defence systems had downed a swarm of attack drones and nearly 20 cruise mislies in Russia's latest aerial barrage overnight.
- 'Sabotage-terrorist acts' -
"A total of 24 strike UAVs (unmanned aerial vehicles) were recorded around the Mykolaiv and Odesa regions. Eighteen attack drones were shot down by air defence units," the air force said on social media.
It added that Kyiv had shown down all 17 cruise missiles fired by Russia.
Russia meanwhile said on Monday it had hit Ukrainian "storage sites" for British Storm Shadow cruise missiles and ammunition with depleted uranium -- a controversial weapon supplied by the United States to Kyiv.
In Russian-occupied Donetsk, authorities reported a Ukrainian strike that damaged the building of the local Moscow-installed administration. The latter said the strike had not caused casualties.
Kyiv is stepping up aerial attacks on Russia.
Moscow said it had repelled Ukrainian drones over outer Moscow and two border regions -- as well as over several parts of occupied Crimea, which Russia annexed from Ukraine in 2014.
Russian cities and Crimea have been targeted throughout the war but Russian officials have downplayed their significance.
In southern Russia, security services said they had arrested two Russian nationals who were preparing "sabotage-terrorist acts" on the orders of the anti-Kremlin nationalist group "Freedom of Russia Legion".
The Ukraine-based group organised a dramatic cross-border incursion into the Russian region of Belgorod in May -- with Moscow even deploying helicopters to quell the push into its territory.
- Chinese diplomat to visit -
The FSB said it detained the two Russian citizens in the southern Rostov region near the border with Ukraine "while they were preparing to set fire to an administrative building".
Rostov was also the scene of an armed rebellion by Wagner mercenary fighters this summer.
Kyiv announced its territorial gains as Beijing said China's top diplomat, Wang Yi, would begin a four-day visit to Russia on Monday for security talks.
China and Russia are strategic allies. Both countries frequently tout their "no limits" partnership and economic and military cooperation.
China's foreign ministry said Wang would hold security consultations at the invitation of Nikolai Patrushev, secretary of Russia's Security Council.
The visit was due a day after North Korean leader Kim Jong Un left Russia following a rare six-day trip, which appeared to solidify his country's ties with President Vladimir Putin and fanned Western fears that Pyongyang could provide Moscow with weapons.
A top United Nations expert meanwhile warned that respect for human rights inside Russia had substantially worsened since Moscow launched its full-scale invasion of Ukraine last year.
"The situation of human rights in the Russian Federation has significantly deteriorated since its invasion of Ukraine in February 2022," UN Special Rapporteur Mariana Katzarova said in her first report on Russia.
Russia has criminalised criticism of the military, and law enforcement officials have detained thousands for protesting or speaking out against the invasion.
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