Ukraine is "still in a state of war" with neighbouring Russia despite a cease-fire between Kiev's forces and Moscow-backed rebels in the east, the country's prime minister said shortly after a second convoy of Russian trucks rolled into Ukraine.

Speaking at a conference with politicians and business leaders in Kiev, Arseniy Yatsenyuk said Russian President Vladimir Putin's goal is "to take the entire Ukraine".

"He cannot cope with the idea that Ukraine would be a part of a big EU family. He wants to restore the Soviet Union," Mr Yatsenyuk said.

He did not mention the second convoy of Russian trucks that entered rebel-held territory in eastern Ukraine earlier on Saturday, reportedly filled with almost 2,000 tons of humanitarian aid.

The last truck crossed onto Ukrainian soil from the Russian border town Donetsk, some 200km east of the Ukrainian city with the same name, Rayan Farukshin, a spokesman for Russia's customs agency, said.

He could not confirm the number of trucks, but news agency ITAR TASS reported that about 250 trucks were heading toward the city Luhansk.

The Russian emergency ministry, which coordinated previous humanitarian aid deliveries to Ukraine, could not be reached for comment about the convoy.

Col Andriy Lysenko, a spokesman for the Ukrainian National Security and Defence Council, told journalists that the convoy had crossed "illegally" onto Ukrainian territory.

"Ukraine border guards and customs were not allowed to examine the cargo and vehicles," he said. "Representatives of the Red Cross don't accompany the cargo, nobody knows what's inside."

Col Lysenko's relatively mild comments on the second convoy and the silence of more senior Ukrainian officials shows how dramatically the mood has shifted in the Kiev government since August.

President Petro Poroshenko has been at pains to prove that last week's cease-fire deal has yielded improvements on the ground in east Ukraine. On Friday, he lauded the deal, which has been riddled by violations since it was imposed last week, as a "fragile but efficient peace process".

In August, Ukrainian officials said that a first convoy of humanitarian aid from Russia would be seen as an invasion of the country, and loudly protested any attempts by Russia to unilaterally bring in the aid.

Eventually Russia sent its trucks across the border and into rebel-held territory without the oversight of the International Red Cross, contrary to an agreement signed between Ukraine and Russia.

A representative of the ICRC's Moscow office said they had not been informed about the current convoy, either.

"We were not officially notified of an agreement between Moscow and Kiev to ship the cargo," Galina Balzamova said.

Col Lysenko said that six Ukrainian servicemen had died since the truce. He also confirmed that 12 rebel fighters had been killed by Ukrainian forces near Sea of Azov city of Mariupol, where he said they were doing reconnaissance work - the first such admission that they have inflicted casualties on the rebel side since the cease-fire began.

In a statement posted online, the Donetsk city council said that there had been fighting near the airport throughout the night. Two shells had hit residential buildings in the area but no casualties were reported.

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