Kiev has said the humanitarian aid might be used as cover for a Russian military intervention, and has insisted that its forces check the convoy before it moves across the border.
Moscow has denied any ulterior motives, but has allowed Ukrainian border guards to enter Russia and look at the caravan of trucks in an area opposite the frontier town of Izvaryne.
"Ukrainian border guards are there already in large numbers," border guard spokesman Andriy Demchenko said. The Ukrainian military said the inspection began on Friday morning, but it was not clear how long the process might take.
On Thursday, the convoy of some 280 trucks stopped in open fields near the Russian town of Kamensk-Shakhtinsky, about 20 km (12 miles) from the border in front of Izvaryne, which is under the control of pro-Russian separatists.
Apart from the trucks, a Reuters reporter at the scene saw a dozen armoured personnel carriers (APCs) on the move not far from the convoy. Another Reuters reporter saw two dozen APCs moving near the border with Ukraine on Thursday night.
The Guardian reported on Friday that its reporter had seen several APCs crossing the border with Ukraine. (bit.ly/1pbRpYg)
Asked about the report, a Ukrainian military spokesman, Oleksiy Dmytrashkivsky, said: "These movements into Ukrainian territory take place practically every day with the aim of provoking (the Ukrainian side). Last night was no exception. Some armoured vehicles came across. We are checking on the quantity and the number of people who came over."
Kiev and NATO have said they fear Russia, which they say has massed more than 40,000 troops near the border, will invade east Ukraine. Russia says it is conducting military exercises and has no plans to invade. It also denies supporting rebels in eastern Ukraine with arms and funds.
The United States and the European Union have imposed sanctions on Russia over its role in east Ukraine and the earlier annexation of Ukraine's region of Crimea, in what has become the worst crisis in relations between Moscow and the West since the Cold War.
Relief agencies say people living in Luhansk and in Donetsk, where pro-Moscow separatists are fighting government forces, face shortages of water, food and electricity after four months of conflict, in which the United Nations says more than 2,000 have been killed.
Russia says its convoy is carrying 2,000 tonnes of water, baby food and other aid for people in the region, and has dismissed accusations by Kiev and some Western officials that it could be a cover for a military infiltration.
Kiev has said if the humanitarian convoy enters Ukraine without the consent of the authorities, the Ukrainian government will view that as an illegal incursion.
However, it appeared likely that a deal could be brokered.
Russia's foreign ministry said it was in intensive talks with the Ukrainian government and the Red Cross, while the Ukrainian foreign ministry said technical agreements had been reached about procedures for inspecting the convoy under the supervision of the Organisation for Security and Cooperation in Europe (OSCE) and the Red Cross.
Kiev blames Russia and the separatists for the plight of the civilians, but their situation has grown more acute as the Ukrainian military has pressed its offensive - including in areas where civilians live.
Artillery shells hit close to the centre of Ukraine's separatist-held city of Donetsk for the first time on Thursday.