Moscow called week-long delays in allowing the vehicles across the border an "outrage" as it ordered the convoy into rebel-held territory, despite Red Cross officials refusing to provide and escort because of security concerns.
"This is a direct invasion," the head of Ukraine's security service, Valentyn Nalyvaychenko, was quoted by news agencies as saying.
Ukraine said all responsibility for the trucks' safety lay with Moscow, after Russia warned "against any attempts to disrupt a totally humanitarian mission."
"The responsibility for any possible consequences of provocations against the humanitarian convoy lie completely with those who are ready to continue to sacrifice human lives for their ambitions and geopolitical plans," the Russian foreign ministry said in a statement.
Russia has been haggling with Ukraine over the convoy amid fears in Kiev and the West that the lorries could be used to bolster a flagging pro-Russian rebellion or provide a pretext for Russia to send in troops.
Russia insists it just wants to get urgently needed assistance to residents in the stricken region who have been without water and electricity for weeks.
Moscow said it was ready to have Red Cross officials accompany the convoy, but the organisation said it had backed out of the operation because of fierce fighting raging in the area where the trucks are heading.
"We are not part of the convoy in any way," Victoria Zotikova, the Red Cross spokeswoman in Moscow, told AFP.
"We have not received sufficient security guarantees from the fighting parties," she said, adding that a small team of Red Cross officials in the rebel bastion of Lugansk reported heavy shelling overnight.
- Border officials 'blocked' -
Ukraine's border service said its officials at the border were effectively "blocked" at the Russian checkpoint as the trucks crossed into Ukraine, violating all prior agreements.
Nearly 300 trucks driven by men in identical beige clothing had been waiting for the green light since arriving at the border over a week ago and progress appeared to be made Thursday when Ukraine said its officials had started checking the convoy.
An AFP photographer at the scene near the border checkpoint between Russia's town of Donetsk and Ukraine's village of Izvaryne saw the first 10 white lorries pass the border guards and drive up to a customs checkpoint on Ukrainian territory.
After four months of fighting that has cost some 2,200 lives, Ukrainian forces have been steadily gaining ground with the rebels now surrounded in several key strongholds and street battles starting in populated areas.
Analysts have said that Kiev and Moscow are both under pressure to strengthen their positions ahead of a meeting between Ukrainian President Petro Poroshenko and Russia's Vladimir Putin next Tuesday in Minsk where EU officials will also be present.
On Thursday Poroshenko said his delegation is going to Minsk to "talk peace" but that "to have strong positions during peace talks, we must be strong".
The presidency said Ukraine will "ask for militants to be taken out of Ukraine" at the meeting, which will also come on the heels of his talks with German Chancellor Angela Merkel who is due in Kiev Saturday.
Russia however has urged Kiev to announce a ceasefire in the conflict area for its convoy to move through the Lugansk region to Lugansk, a city hardest hit in the conflict and suffering after nearly three weeks without water, power or communication.
'Considerable' rebel losses
Kiev's security forces on Friday said the military has gained ground further against the separatists, with the press-service for its operation in the east reporting "considerable enemy losses".
But Kiev also said that pro-Russian rebels shot down a Ukrainian air force helicopter on Wednesday near Lugansk, killing the two-member crew.
Meanwhile, in the southwestern outskirts of the largest rebel-held city of Donetsk, a separatist checkpoint was shelled on Friday by Kiev's forces positioned nearby.
"We hid in a cellar," said Valentina, who was woken up by the blasts at 4:30 am. "It was really scary. Whoever did it, God will be their judge."
"If I only knew where to shelter my children and grandchildren," she added, showing pieces of shrapnel and broken glass littering her house.
Nearby, residents of the neighbourhood where the taps have been cut off due to fighting stood in line with water canisters.
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Ukraine accuses Russia of ''invasion'' as aid trucks move in