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With Ukraine reporting Russia has massed 45,000 troops on its border, NATO said there was a "high probability" that Moscow could intervene militarily in the country's east, where Kiev's forces are closing in on pro-Russian separatists.
Western countries believe that Putin - who has whipped up the passions of Russians with a nationalist campaign in state-controlled media since annexing Crimea from Ukraine in March - could now send his forces into the east to head off a humiliating rebel defeat.
Thousands of people are believed to be short of water, electricity and medical aid due to the fighting, but U.S. President Barack Obama told his Ukrainian counterpart that any Russian intervention without Kiev's consent would be unacceptable and violate international law.
European Commission President Jose Manuel Barroso delivered a blunter message directly to Putin in a telephone call on Monday. "President Barroso warned against any unilateral military actions in Ukraine, under any pretext, including humanitarian," the Commission said in a statement.
The Kremlin, in its own account of the conversation, made clear that Moscow would indeed send help to largely Russian-speaking eastern Ukraine.
"It was noted that the Russian side, in collaboration with representatives of the International Committee of the Red Cross, is sending an aid convoy to Ukraine," the Kremlin statement said, without revealing when the convoy was going.
In a cautious response, the International Committee of the Red Cross (ICRC) said it had submitted a document to Russian and Ukrainian officials on delivering aid. However, the independent agency stressed in a statement that it needed agreement from all parties as well as security guarantees to carry out the operation, as it does not use armed escorts.
"The practical details of this operation need to be clarified before this initiative can move forward," said Laurent Corbaz, head of ICRC operations for Europe and Central Asia.
According to U.N. agencies, more than 1,100 people have been killed including government forces, rebels and civilians in the four months since the separatists seized territory in the east and Kiev launched its crackdown.
UKRAINE SEEKS INTERNATIONAL EFFORT
Ukrainian President Petro Poroshenko came out in support of an aid mission but made clear it had to be an international effort under the aegis of the ICRC, involving the European Union as well as Russia.
He won Obama's backing when they spoke by phone on Monday. The White House quoted Obama as saying that any Russian intervention without the Ukrainian government's agreement would be "unacceptable" and a violation of international law.
Earlier, Kiev said it was in the "final stages" of recapturing the eastern city of Donetsk - the main base of the separatist rebels - in a battle that could mark a turning point in a conflict that has caused the biggest confrontation between Russia and the West since the Cold War.
An industrial metropolis with a pre-war population of nearly 1 million, Donetsk rocked to the crash of shells and gunfire over the weekend, and heavy guns boomed through the night into Monday from the outskirts of the city.
NATO Secretary-General Anders Fogh Rasmussen said there was no sign Russia had withdrawn the troops it had massed at the Ukrainian frontier. Asked in a Reuters interview how he rated the chances of Russian military intervention, Rasmussen said: "There is a high probability."
"We see the Russians developing the narrative and the pretext for such an operation under the guise of a humanitarian operation, and we see a military build-up that could be used to conduct such illegal military operations in Ukraine," he said.
SAVING THE REBELS
NATO fears Moscow would use any aid mission as a cover to save the rebels, who are fighting for control of two provinces under the banner of "New Russia", a term Putin has used for southern and eastern Ukraine, where mostly Russian is spoken.
Ukraine appears to be pressing ahead with its offensive, undeterred by the presence of what NATO says are about 20,000 Russian troops massed on the nearby border for a potential ground invasion.
Kiev put the size of the Russian forces much higher. "As of 11 o'clock today, about 45,000 troops of the armed forces and internal forces of the Russian Federation are concentrated in border areas," Ukrainian military spokesman Andriy Lysenko told a briefing.
He said they were supported by 160 tanks, 1,360 armoured vehicles, 390 artillery systems, up to 150 Grad missile launchers, 192 fighter aircraft and 137 attack helicopters.
Lysenko said Ukrainian government forces had finally succeeded in cutting off the road between Donetsk and Luhansk, the other main rebel-held city, which is closer to the Russian border. Kiev and its Western allies say the route has been the principal means of supplying the rebels in Donetsk with weapons.
Fighting in recent weeks has focused on the route, near where Malaysia Airlines flight MH17 crashed in July, killing all 298 people on board. Washington says the plane was almost certainly shot down accidentally by rebels using an advanced Russian missile. Moscow denies this.
"The forces of the anti-terrorist operation are preparing for the final stage of liberating Donetsk," Lysenko told Reuters. "Our forces have completely cut Donetsk off from Luhansk. We are working to liberate both cities, but it's better to liberate Donetsk first - it is more important."
The leader of the rebels in Donetsk, Alexander Zakharchenko, a local man who took over the leadership from a Russian citizen last week, said the fighters were considering mounting a counter-attack against government forces in the next two or three days.
And a volunteer government fighter suggested claims that government forces were about to take Donetsk were inflated. "Taking the town is an extremely complicated business and painful ... It will take, at the very least, several weeks," said Andriy Beletsky, commander of the so-called Azov battalion.
Municipal authorities in Donetsk said artillery shelling knocked out power stations in the city and hit a high-security prison, killing one inmate and allowing more than 100 criminals to escape.