A Russian aid convoy is returning to Russia, after sparking anger from Western leaders when it entered Ukraine without Kiev's permission on Friday.

The first of the 220 trucks began crossing back into Russia's borders on Saturday, after Western leaders joined Ukraine's government in condemning the convoy's entry as an illegal incursion into Ukrainian territory.

At least 10 trucks loaded with bottled water and tinned food have passed back into Russia from the Donetsk-Izvarino border crossing, where the convoy entered Ukraine on Friday, Reuters reported.

Russian state television broadcast footage of some of the trucks being unloaded at a distribution depot in the eastern Ukrainian rebel-held city of Luhansk, after Russia's foreign ministry said the convoy – which had been stuck at the border for more than a week – could not wait any longer.

The vehicles passed through a Ukrainian border post controlled by pro-Russia fighters, prompting Kiev to demand the convoy's immediate withdrawal.

In a phone call with German chancellor Angela Merkel on Friday, Russian president Vladimir Putin said Moscow decided to send the aid lorries because of Kiev's "obviously stalling".

In a statement, Russia's foreign ministry said Kiev was "deliberately dragging out the delivery of the humanitarian aid", so it could carry out a "military cleansing of Luhansk and Donetsk" by Independence Day celebrations on Sunday.

Ukraine: Russian Aid Convoy Checked by Red Cross
A Russian aid lorry is checked by the Red Cross.

The arrival of the aid convoy was swiftly condemned by the EU and the US, with the White House warning of "additional consequences" if Russia did not comply.

Deputy national security adviser Ben Rhodes said in a media briefing from President Obama's vacation home on Martha's Vineyard: "We very much condemn this flagrant violation of Ukrainian sovereignty which we saw today with the movement of this Russian convoy into Ukraine.

"We will be in touch today with our partners on the United Nations security council to discuss next steps. Russia should take the opportunity to remove this convoy from within Ukraine. If they don't, they will face additional costs and consequences from the US and our partners in the international community."

The US also accused Russia's military forces of repeatedly firing into Ukrainian territory, and suggested that the aid convoy could be a "pretext" for further escalating the conflict with Ukraine.

However, Vitaly Churkin, Russia's ambassador to the United Nations, told a press conference that the aid convoy had received permission from Kiev to enter the Ukraine's disputed territory.

Pro-Russian separatists are now encircled in their two strongholds, Luhansk and Donetsk, where heavy shelling could be heard early on Saturday.

Nato said it had evidence that Russian forces had been firing artillery at Ukrainian government troops in Ukraine. The announcement fuels allegations by Western leaders that the Kremlin is stoking the conflict in an effort to undermine Kiev's Western-friendly leadership.