Russia said Monday it had repelled "a large-scale offensive" by Ukrainian forces in the Moscow occupied Donetsk region as Kyiv was silent about plans to claw back lost territory.
Ukrainian officials meanwhile were expected to hold talks with Pope Francis' peace envoy, Italian Cardinal Matteo Zuppi, who headed to Kiev Monday for two days of negotiations.
Ukraine says it has been preparing a major offensive after months of stalemate to recapture territory lost since Russian President Vladimir Putin sent troops in February last year.
But officials have been tight-lipped about the details, saying there would be no formal announcement about the start of the operation.
On Sunday, Ukrainian Defence Minister Oleksiy Reznikov posted a cryptic tweet, citing lyrics from Depeche Mode's song, "Enjoy the Silence."
"Words are very unnecessary," he tweeted. "They can only do harm."
Military experts expect Ukrainian forces to test Russian defences for weaknesses before starting a full-blown offensive.
Early Monday, Russia's defence ministry said that on Sunday "the enemy launched a large-scale offensive in five sectors of the front" in the south of the Donetsk region.
"A total of six mechanised and two tank battalions of the enemy were involved," it said in a Telegram post, adding that Ukrainian troops had hit "the most vulnerable, in their opinion, sector of the front".
"The enemy did not achieve their tasks, they had no success."
The ministry posted what it said was a video of the battle, showing Ukrainian armoured vehicles coming under heavy fire.
Putin's top commander in Ukraine, Valery Gerasimov, "was at one of the advanced command posts," the ministry said.
A high-profile Russian war correspondent, Alexander Kots, said that "battles have been going on" in the area of Ugledar, in the south of the Donetsk region, and also further north in Soledar and Bakhmut, which were occupied by Moscow's forces after months of fighting.
Kots said Ukrainian forces were "conducting offensive operations" in and around the frontline hotspot of Bakhmut which Russian mercenary group Wagner claimed last month had fallen to Moscow.
He suggested that Kyiv had not yet "introduced the main forces into battle."
- 'The fight will be serious' -
A Moscow-installed official also said that Ukrainian troops were on the offensive in the southern region of Zaporizhzhia, home to Europe's largest nuclear plant, which has been under control of Russia's forces since the start of Moscow's offensive.
"It looks like the die has been cast and the next couple of months will clear up a lot. The fight will be serious, because there is a lot at stake," Rogov added.
Large parts of Donetsk have been held by pro-Moscow separatists since 2014. It is one of four eastern Ukrainian territories that Russia formally annexed in September last year, along with Lugansk, Zaporizhzhia and Kherson.
Speaking to reporters in New Delhi, US Secretary of Defense Lloyd Austin said that Ukrainian authorities would make an announcement "at the right time".
"We can talk about what we're seeing and we're seeing continued operations in and around the Bakhmut area," he added.
"We're seeing an uptick in activity south of there."
- Pope's envoy in Kyiv -
The Vatican said that Italian Cardinal Matteo Zuppi headed to Kiev Monday as Pope Francis' peace envoy for talks with Ukrainian authorities on the war.
Zuppi, the head of the Italian bishops' conference, "will pay a visit to Kyiv as Envoy of the Holy Father" from June 5 to 6, it said in a statement.
The Russian army claimed to have repelled a "sabotage group of Ukrainian terrorists" seeking to cross the border near the village of Novaya Tavolzhanka, in the southern region of Belgorod.
Belgorod's governor said Sunday that fighting took place near Novaya Tavolzh
"The enemy was hit by artillery. The enemy scattered and retreated," it said in a statement.
anka, and acknowledged pro-Ukrainian forces had taken Russians prisoner during cross-border clashes.
It was the first time during the more than 15 months of conflict that a Russian official has admitted the capture of prisoners on Russian territory by pro-Ukraine forces.
Fighting around the village follows last month's dramatic armed incursion from Ukraine into the Belgorod region which forced Russia to use its artillery and air force on home soil.
The border breach was claimed by anti-Kremlin Russian ultra-nationalists.
Ukraine has consistently not claimed responsibility for attacks on Russian soil, but presidential adviser Mykhaylo Podolyak said Sunday the situation in the border areas "should be viewed as the future of Russia".