Ukrainian border guards are expected to begin checking some of the cargo of a Russian aid convoy on August 21.
Four Russian trucks from the 260-strong convoy moved into the customs zone near the Ukrainian border on August 20.
Andriy Lysenko, a spokesman for Ukraine's National Security Council, said cargo checks could not start right away because Russia had not provided all the necessary documents.
The convoy has been stuck at the Russia-Ukraine border for nearly a week due to Ukrainian concerns it could be used to infiltrate military supplies to pro-Russian separatists in eastern Ukraine.
Moscow says the mission is purely humanitarian in support of civilians trapped by the conflict.
Red Cross officials entered eastern Ukraine on August 20 to smooth the planned delivery of the relief supplies.
Red Cross officials and vehicles are expected to accompany the Russian trucks and their drivers once they get the green light.
Meanwhile, fighting is reported to be continuing in and around the rebel strongholds of Donetsk and Luhansk.
After days of street fighting, Lysenko said government forces are now controlling "significant parts" of Luhansk.
Luhansk has been largely cut off for weeks and is without water and regular supplies of electricity.
Reports late on August 20 spoke of fresh shelling of residential neighborhoods in Donetsk.
AFP journalists reporting from Donetsk said shells had landed in the city center near the home stadium of the football club Shakhtar Donetsk.
The attacks came after reports on August 20 said 34 people were killed in fighting in the Donetsk area in the previous day.
Lysenko also said fighting had continued on August 20 in nearby Ilovaysk, despite government forces taking overall control of the town following fighting on August 19.
Lysenko said among the nine troops killed in Ilovaysk was a Ukrainian-American, Mark Gregory Paslawsky, who fought under the nom de guerre "Franko."
The United Nations says more than 2,000 people, including civilians and combatants, have died in the conflict.
That figure has nearly doubled since late July, when Ukrainian forces stepped up their offensive and the fighting spread to major urban areas in eastern Ukraine.
With reporting by ITAR-TASS, Reuters, and AFP