The trucks seem unlikely to cross into Ukraine immediately as the Red Cross said it had still not received security guarantees for the convoy to continue.
Earlier Ukraine’s military said that separatists had shot down a government fighter jet near the rebel-held city of Luhansk in the east of the country.
A military spokesman said the pilot had ejected and was safe.
More than 2,000 civilians and combatants have been killed since mid-April, when Ukraine’s government sent troops to put down an uprising by pro-Russian separatists in the Donetsk and Luhansk regions.
It faced a new challenge on Sunday as the leader of the ultra-nationalist Right Sector threatened to withdraw volunteers fighting on the government side.
Dmytro Yarosh said Right Sector would launch a “campaign in Kiev” if its demands, including the release of detained members, were not met within 48 hours.
He called on President Petro Poroshenko to “immediately bring order” to the Interior Ministry, which he accused of harboring “revanchist forces”.
The government plane had been shot down after launching an attack “to eliminate a large group of rebels”, Ukrainian military spokesman Leonid Matyukhin said, quoted by AFP news agency.
The pilot ejected from the aircraft safely and rescuers delivered him to a safe location, the spokesman added.
Meanwhile some 16 vehicles from the 280-lorry Russian convoy carrying humanitarian aid for eastern Ukraine were seen arriving at the border.
The Red Cross, quoted by Reuters news agency, said Ukrainian and Russian customs officials had agreed to inspect the lorries.
The Izvaryne crossing where the vehicles have arrived is controlled by rebels, so it is not clear how Ukrainian officials will reach them.
Kiev has insisted that any aid sent to eastern Ukraine from Russia should cross a government-controlled part of the border.
Also, Ukraine’s Security Council tweeted that its border guards had not received any paperwork for the cargo.
The convoy has been parked near the town of Kamensk-Shakhtinsky for several days after setting out from near Moscow on Tuesday, said to be carrying 2,000 tonnes of aid.
Russian officials quoted by Russia’s Ria news agency said that lorries were being sent out in small groups to avoid causing traffic jams, but there were no plans for any of them to cross the border on Sunday.
The Ukrainian government said late on Saturday that it had declared the convoy “legal”, but Red Cross officials speaking at the time said it had still not been given clearance because of some outstanding security issues.
There had been fears expressed by Ukraine and by Western governments that the convoy could be carrying arms for the rebels or could be used as a pretext by Russia for military action.
Russia has denied any military involvement with the convoy.
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