The claim came hours before Pope Francis' peace envoy, Italian Cardinal Matteo Zuppi, arrived in Kiev 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 into the country in February last year.

But Kyiv, which has been reinforced by supplies of advanced Western weapons, said there would be no formal announcement about the start of the offensive.

On Sunday, Ukrainian Defence Minister Oleksiy Reznikov posted a cryptic tweet, quoting lyrics from Depeche Mode's song "Enjoy the Silence".

"Words are very unnecessary," he tweeted. "They can only do harm."

The Ukraine conflict has escalated in recent weeks, with increased attacks on both sides of the border with Russia.

Military experts expect Ukrainian forces to test Russian defences for weaknesses before starting a full-blown offensive.

Early on Monday, Russia's defence ministry said "the enemy launched a large-scale offensive in five sectors of the front" on Sunday 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.

"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, Chief of the General Staff Valery Gerasimov, "was at one of the advanced command posts", the ministry said.

The claims could not be independently verified.

A high-profile Russian war correspondent, Alexander Kots, said "battles have been going on" around Ugledar, in the south of the Donetsk region, and 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 Bakhmut, which mercenary group Wagner last month claimed had fallen to Moscow.

Kots suggested Kyiv had not yet "introduced the main forces into battle".

Pro-Moscow war blogger Alexander Khodakovsky said Ukrainian troops had deployed Leopard tanks in the east.

- 'Disgrace' -

Wagner boss Yevgeny Prigozhin said on Monday that Ukraine's troops had made gains near Bakhmut.

Russian troops, he said, were leaving the village of Berkhivka near Bakhmut.

"Disgrace!", he said, challenging Russian Defence Minister Sergei Shoigu to come to the front.

"Come on! You can! And if you can't, die a hero," he said.

A Moscow-installed official said Ukrainian troops were on the offensive in the southern region of Zaporizhzhia, home to Europe's largest nuclear plant, which has been under the 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," Vladimir Rogov said.

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 the 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.

- Pope's envoy in Kyiv -

The Vatican said that Pope Francis' peace envoy, Italian Cardinal Matteo Zuppi, had headed to Kiev on Monday for talks on the war with the Ukrainian authorities.

Zuppi, the head of the Italian bishops' conference, "will pay a visit to Kyiv as envoy of the Holy Father" on June 5 and 6, the Vatican said.

In recent days, strikes have intensified in Russia's southern Belgorod region, where there has been shelling and cross-border incursions.

On Monday, several Russian radio stations were hacked and played a fake President Vladimir Putin speech announcing an invasion by Kyiv's troops and emergency measures in three regions bordering Ukraine, the Kremlin said.

The Russian army claimed to have repelled "Ukrainian terrorists" seeking to cross the border near the village of Novaya Tavolzhanka, in Belgorod, on Sunday.

Fighting around the village followed last month's dramatic armed incursion into Belgorod from Ukraine, which forced Russia to use its artillery and air force on home soil.

The border breach was claimed by Russian anti-Kremlin ultra-nationalists.

Ukraine has consistently denied responsibility for cross-border attacks on Russian soil.