The first trucks in a Russian aid convoy crossed into eastern Ukraine on Friday, seemingly without Kiev's approval, after more than a week's delay amid suspicions the mission was being used as a cover for an invasion by Moscow.

Trucks loaded with water, generators and sleeping bags are intended for civilians in the city of Luhansk, where pro-Russian separatist fighters are besieged by government forces. Shelling of the city has been ongoing for weeks.

An Associated Press reporter saw a priest blessing the first truck in the convoy and then climbing into the passenger seat. At least 16 trucks had traveled into Ukraine, but their immediate destination was not known and it was not clear whether Kiev had granted its approval.

"The Russian side has decided to act," said a statement on the Russian foreign ministry's website. "Our column with humanitarian aid is starting to move in the direction of Luhansk."

The Red Cross has said it needs assurances of safe passage from all sides to bring in the supplies and it was unclear whether they accompanied the trucks heading into Ukraine.

The Russian statement said that the Red Cross is "ready" to accompany the convoy, but none of their staff were immediately visible Friday.

The relief supply mission is proceeding despite both Ukraine and the separatists ignoring pleas for a cease-fire.

A rebel commander on the scene who identified only by the codename Kot said the trucks were headed for the city of Luhansk.

The trucks loaded with humanitarian aid sent from Moscow had been stranded in a customs zone for more than a week since reaching the border, as the Russian foreign ministry voiced increasing frustration at what it said were Kiev's efforts to stall its delivery.

Rayan Farukshin, a spokesman for Russia's customs control, told the AP that 34 Russian vehicles had been approved for onward travel through Ukraine on Thursday. But Russia's foreign ministry blasted the Ukrainian side for "endless, concocted delays" in delivering the aid, which left Moscow early last week.

It blamed the Kiev government for continuing to shell residential areas that the convoy would have to pass through, thereby making its onward travel impossible.

"There is increasingly a sense that the Ukrainian leaders are deliberately dragging out the delivery of the humanitarian load until there is a situation in which there will no longer be anyone left to help."