Russia's defence ministry said that "high-precision air-based missiles" had hit 13 Ukrainian positions in parts of the Donbas while other air strikes "hit 60 military assets", including in towns close to the eastern frontline.

Ukraine's armed forces also confirmed that fighting had increased throughout the east just hours after President Volodymyr Zelensky said Russia had kicked off the widely anticipated offensive in the Donbas region on Monday.

"The Russian occupiers intensified offensive operations along the entire line of contact," the general staff of Ukraine's armed forces said in a report published early Tuesday.

Later Tuesday, Russia's defence chief stopped short of confirming any new offensive but said his forces were committed to capturing swathes of eastern Ukraine.

"We are gradually implementing our plan to liberate the Donetsk and Lugansk People's Republics," Sergei Shoigu said referring to eastern Ukraine's two rebel regions, which Moscow has recognised as independent states.

"We are taking measures to restore peaceful life," he said in a televised meeting with Russian military commanders.

Ahead of the advance, Ukrainian authorities had urged people in Donbas to flee west to escape, even as officials called off evacuations for a third straight day from frontline cities due to ongoing fighting.

"No matter how many Russian soldiers are brought here, we will fight. We will defend ourselves," Zelensky said on Telegram late Monday.

In the Donbas town of Novodruzhesk, Nadya, 65, said "we are bombed everywhere".

"It's a miracle that we're still alive," she said, her voice trembling.

"We were lying on the ground and waiting. Since February 24 we've been sleeping in the cellar."

Control of Donbas would allow Moscow to create a southern corridor to the occupied Crimean peninsula.

However, Zelensky's advisor Oleksiy Arestovich offered an alternate view during an interview on Ukrainian television Tuesday, saying the offensive in the Donbas had been ongoing for 12 days.

"They advance by looking for weak points in our defences. As soon as they find them, they infiltrate them," he added.

In the south, Russia continued its push to capture the besieged port city of Mariupol, as Moscow issued a fresh call for the city's defenders to surrender.

But despite the desperate situation in the city, a senior US Defence Department official on Monday said Mariupol "is still contested".

- $800 million boost -

The first shipments of a new $800-million (740 million euros) US military aid package had begun to arrive at Ukraine's borders this week, for use against Russian forces.

Washington was due to hold a video meeting with allies Tuesday to discuss the conflict in Ukraine, even as it increasingly provoked the ire of Moscow.

"The United States and Western states under its control are doing everything to drag out the military operation for as long as possible," said Russia's defence chief Shoigu on Tuesday.

"The growing volume of foreign weapons supplies graphically demonstrate their intention to provoke the Kyiv regime to fight to the last Ukrainian."

His comments came as government sources in Spain said Prime Minister Pedro Sanchez was planning to travel to Kyiv "soon" but did not confirm when for security reasons.

While much of the focus has remained in Ukraine's east, Moscow has also targeted the country's west with air strikes, killing at least seven people in the city of Lviv near the Polish border on Monday.

Lviv has largely been spared bombardment since Russia invaded on February 24, and the city and its surroundings had become a haven for those seeking safety from the war zone.

But even as strikes continued to hit targets across the country, the east appeared to be Russia's primary focus.

The regional governor of the eastern Lugansk region Sergiy Gaiday said Ukrainian forces continued to hold their ground amid heavy fighting.

"We have positional battles in the cities of Rubizhne and Popasna. The enemy cannot do anything though. They are losing people and equipment there," Gaiday said.

"Our guys are shooting down drones there. Shooting down planes on the border of the Lugansk and Kharkiv regions, so they are holding on," he added.

- 'Heavy attacks' -

Russian President Vladimir Putin has said he launched the so-called military operation on February 24 to save Russian speakers in Ukraine from a "genocide" carried out by a "neo-Nazi" regime.

On Monday, Putin lauded the 64th Motor Rifle Brigade -- which is accused of committing atrocities near Kyiv -- bestowing battle honours on them for "heroism and valour, tenacity and courage".

Ukraine has alleged the brigade committed war crimes while occupying the suburb of Bucha on the outskirts of Kyiv, where residents were shot dead, some with their hands bound.

The European Union condemned Russia's "indiscriminate" bombing of Ukrainian civilians.

Its foreign policy chief Josep Borrell pointed to "particularly heavy attacks" in eastern and southern Ukraine and an offensive against second city Kharkiv, where officials said Russian shelling killed three people.

Seeking to strengthen ties and accelerate its admission to the 27-nation bloc, Zelensky said that Ukraine hoped to receive EU candidate country status within weeks.

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