Security council spokesman Andriy Lysenko said the Russian aid should pass through a government-controlled border post and be accompanied by Red Cross officials.
There are Western concerns that Russia is using humanitarian assistance as a pretext to invade eastern Ukraine.
At least 1,500 have died since Ukraine sent troops against pro-Russia rebels.
The fighting in the Donetsk and Luhansk regions since mid-April has displaced hundreds of thousands of people, many of whom have fled to Russia.
The Red Cross says it still needs more security guarantees and information about the aid convoy.
Almost 300 trucks of humanitarian aid left the Moscow area bound for Luhansk on Tuesday morning.
Russian TV showed the cargo, said to include hundreds of tonnes of grain, baby food and medicine, which will go to civilians trapped by fighting in the area held by pro-Russia rebels.
Media reports said the cargo left from a point south-west of Moscow. It is expected to arrive at the Ukrainian border in the next two days.
“The convoy will deliver to the residents of eastern Ukraine about 2,000 tonnes of humanitarian cargo, collected by the residents of Moscow city and region,” Moscow region officials said.
Andriy Lysenko said Ukraine had three conditions for receiving the aid:
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