Around 70 lorries from what Russian says is an aid convoy crossed the border with Ukraine on Friday, heading towards Luhansk in eastern Ukraine.
Witnesses say they were accompanied by a small number of pro-Russian fighters.
The Russian foreign ministry confirmed that the convoy was heading towards Luhansk and said they were “ready for the Red Cross to participate in the aid distribution”.
Ukraine will not attack the convoy and wants to avoid any “provocations”, Ukrainian state security chief Valentyn Nalivaychenko said.
“Ukraine will liaise with the International Committee of the Red Cross so that we, Ukraine, are not involved in (accusations of) provocations that we have been holding up or using force against the vehicles of so-called aid,” he told journalists.
Moscow accuses Kyiv of deliberately delaying the delivery of humanitarian supplies.
More than 260 lorries carrying food and medicines have been stuck at the border for more than a week.
Many of the lorries arrived empty, sparking speculation that they were not intended for aid delivery and had instead been deployed for another, as yet unknown, reason.
Interfax news agency says a Ukrainian government source confirmed that the convoy did not have authorisation to enter Ukraine, and it is not accompanied by members of the Red Cross.
Moscow says the aid is intended to alleviate a humanitarian crisis in the city of Luhansk.
Ukraine claims the convoy could cover the supply of military equipment to the rebels, or be used to ship out dismantled assembly lines from key defence industries located in eastern Ukraine.