The Russian Foreign Ministry had said Wednesday that the convoy of around 280 trucks, which it says is carrying food, water, sleeping bags and other essentials for the civilian populations trapped in Luhansk and Donetsk, would cross the border at Shchebekino, in the Ukrainian government-held region of Kharkiv, in coordination with the authorities in Kyiv and the International Commission of the Red Cross.

However, Ukrainian Interior Minister Arsen Avakov had appeared to backtrack from an earlier, tentative agreement, saying Kyiv would not let any Russian convoy onto its territory, and that “provocation by the cynical aggressor” would be blocked. “No ‘humanitarian convoy’ of Putin’s will be allowed to cross the territory of the Kharkiv region.”

The Associated Press reported that the convoy had taken the road south Thursday morning in the direction of the Russian city of Rostov-on-Don, from where it would more likely enter rebel-held territory around Luhansk.

The Ukrainian government suspects the Russians of using the aid convoy as a pretext for moving in military personnel. The U.S. has warned Russia that it will view any unauthorised incursion into Ukraine as an invasion.

A spokesman for the Red Cross told Fortune Thursday that the organization still hasn’t received a detailed breakdown of the shipments or confirmation of any agreement between the two sides over the convoy’s passage, meaning that it can’t assume responsibility for the convoy, as it had hoped.

“We’re waiting for clarity,” he said.

Both Ukrainian forces and rebels report heavy fighting in the rebels’ two last strongholds, which have now been encircled. Tens of thousands of civilians are reported to have fled, while those who have remained have been without electricity and water supplies for over a week.