Sixteen Russian aid convoy vehicles have driven from the field where they have been parked up since Friday to the Ukrainian border.
They are now in a bus depot near a crossing controlled by pro-Russian separatists, apparently awaiting further inspections.
Russian officials could not give a timetable for when they might enter eastern Ukraine.
One of the lorry drivers explained: “We are bringing food, water, medicine, baby food, everything that the civilian population needs. We’re now waiting for our orders. As soon as we get the go-ahead, we’ll set off. I can’t tell you anything more.”
Asked if he was a member of military, he said: “No I’m not military, I’m a driver.”
The International Committee of the Red Cross, which is due to distribute the humanitarian aid says Ukrainian and Russian customs officials have agreed on inspections of the trucks but the main hold-up is a lack of security guarantees from all sides in the conflict.