Multiple explosions could be heard late on Saturday in the centre of the separatist-controlled city of Donetsk in eastern Ukraine, a Reuters reporter said.
The origin of the explosions was not clear. There was no immediate comment from separatist authorities or from Kyiv.
Two regions in eastern Ukraine where government and separatist forces have been fighting since 2014 were hit by more than 1,400 explosions on Friday, monitors for the Organisation for Security and Cooperation in Europe (OSCE) said, pointing to a surge in shelling.
The two Russian-backed, self-proclaimed republics in Ukraine's Donetsk and Luhansk regions are at the centre of a surge in tensions between Moscow and the West over a vast Russian military buildup near Ukraine.
The OSCE's Special Monitoring Mission that is deployed in the conflict zone confirmed one civilian casualty in a government-controlled area of Donetsk.
Shelling allegations
Separatist leaders in eastern Ukraine have declared a full military mobilisation after ordering women and children to evacuate to Russia, citing the threat of an imminent attack by Ukrainian forces, which Kyiv denied.
Kyiv and Western leaders say the mobilisation, evacuation and increased shelling are part of a Russian plan to create a pretext for an invasion.
Russia's FSB security service said two shells landed on Russian territory near the border, Russia's Tass news agency reported. One hit a building in Rostov region but no one was hurt, it said.
Ukraine's military accused Russia of faking pictures of shells to make out they were Ukrainian, and said mercenaries had arrived in separatist-held eastern Ukraine to stage provocations in collaboration with Russian special forces.
Ukraine's foreign minister demanded an independent international investigation of the alleged incidents in Rostov and the military said two soldiers had been killed in shelling by pro-Russian separatists in east Ukraine.
Russian news agencies said 10,000 evacuees had arrived in Russia. Separatist leaders say they aim to evacuate 700,000 people.
'Poised to strike'
Russia's strategic nuclear forces held exercises overseen by President Vladimir Putin on Saturday, and Washington accused Russian troops massed near Ukraine's border of advancing and being "poised to strike".
With Western fears of war rising, foreign ministers from the G7 group of rich nations said they had seen no evidence Russia is reducing its military activity in the area and remained "gravely concerned" about the situation.
Also on Saturday, a Nato official said the alliance relocated staff from Kyiv to the western city of Lviv and to Brussels for safety reasons. The United States and many other countries have moved diplomats to Lviv.
After Kyiv and Moscow traded accusations over the shelling near the border, France and Germany urged all or some of their citizens in Ukraine to leave. US Defense Secretary Lloyd Austin said Russian forces were beginning to "uncoil and move closer" to the border.
"We hope he (Putin) steps back from the brink of conflict," Mr Austin told a news conference in Lithuania, saying an invasion of Ukraine was not inevitable.
Russia ordered the military build-up while demanding Nato prevent Ukraine from ever joining the alliance but says Western warnings that it is planning to invade Ukraine are hysterical and dangerous. Moscow says it is pulling back, but Washington and allies say the build-up is mounting.
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Venting his frustration at a security conference in Munich, Ukrainian President Volodymyr Zelenskiy said the global security architecture was "almost broken". He urged the permanent members of the UN Security Council, Germany and Turkey to meet to draw up new security guarantees for his country.
"The rules that the world agreed on decades ago no longer work," Mr Zelenskiy said. "They do not keep up with new threats. Not effective for overcoming them. This is a cough syrup when you need a coronavirus vaccine."
The Kremlin said Russia had successfully test-launched hypersonic and cruise missiles at sea during the strategic nuclear forces' military exercises. Putin observed the exercises on screens with Belarusian leader Alexander Lukashenko from what the Kremlin called a "situation centre".
US President Joe Biden said on Friday he believed Putin would invade Ukraine in the coming days.
