Ukraine's army has said two of its soldiers died in attacks on the frontline with Russian-backed separatists - the first fatalities in the conflict in more than a month.
"As a result of a shelling attack, two Ukrainian servicemen received fatal shrapnel wounds," the military command for separatist conflict said.
With Western nations fearing what could be one of the worst conflicts since the Cold War, US Defense Secretary Lloyd Austin said Russian forces were beginning to "uncoil and move closer" to the border with its former Soviet neighbour.
"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 ever joining the alliance but says Western predictions that it is planning to invade Ukraine are wrong and dangerous. It says it is now pulling back.
Washington and allies say the build-up is mounting.
At the Munich Security Conference today, NATO chief Jens Stoltenberg has said all signs suggest Moscow is readying for a "full-fledged attack" on Ukraine.
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Russian-backed separatist leaders in eastern Ukraine declared a full military mobilisation after ordering women and children to evacuate to Russia, citing the threat of an imminent attack by Ukrainian forces.
Kyiv denied the accusation. It and Western leaders say the mobilisation, evacuation and increased shelling across the ceasefire line this week are part of a Russian plan to create a pretext for an invasion of Ukraine.
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 foreign minister denied any Ukrainian shells had hit Russian territory and demanded an independent international investigation of the alleged incidents.
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 Russia's special services.
"The purpose of these provocations will, of course, be to accuse Ukraine of further escalation," it said.
Multiple explosions were heard today in the north of the separatist-controlled city of Donetsk in eastern Ukraine, as more people got on buses to leave, a Reuters witness said. The origin of the explosions was not immediately clear. Ukraine said one of its soldiers had been killed.
"It's really scary. I've taken everything I could carry," said Tatyana, 30, who was boarding a bus with her 4-year-old daughter.
US President Joe Biden said on Friday he believed the capital Kyiv would be targeted by Russia but that he did not think Mr Putin was contemplating using nuclear weapons.
Mr Biden said Mr Putin would invade in the coming days.
"As of this moment, I am convinced that he has made the decision."
The Kremlin said Russia had successfully test-launched hypersonic and cruise missiles at sea at land-based targets during its military exercises.
Mr Putin observed the exercises on screens with Belarusian leader Alexander Lukashenko from what the Kremlin called a "situation centre".
Mr Austin said the nuclear exercises were stoking concern among defence leaders around the world as Russia's military was focused on a huge build-up of forces around Ukraine and there was a danger of "an accident or a mistake".
The drills follow manoeuvres by Russia's armed forces in the past four months that have included a build-up of troops – estimated by the West to number 150,000 or more - to the north, east and south of Ukraine.
Moscow-based analysts said the exercises were aimed at sending a message to take Russia's demands for security guarantees from NATO seriously after the alliance's expansion to Russia's borders since the collapse of the Soviet Union in 1991.
"Ignoring Russia's legitimate rights in this area adversely affects the stability not only on the European continent, but also in the world," Russian Foreign Minister Sergei Lavrov was quoted by his ministry as telling France's foreign minister by phone.
NATO Secretary-General Jens Stoltenberg said Russia knew the alliance could not meet its demands, which include the withdrawal of NATO forces from former communist east European states that have elected to join NATO.
New helicopters and a battle group deployment of tanks, armoured personnel carriers and support equipment have deployed in Russia, near the border, according to US-based Maxar Technologies, which tracks developments with satellite imagery.
The Kremlin also has troops staging exercises in Belarus, north of Ukraine, that are due to end on Sunday. Mr Lukashenko said on Friday they could stay as long as needed.
