Ukraine's President Petro Poroshenko has accused Russia of a "flagrant violation of international law" after Russian humanitarianaid lorries entered Ukraine without permission.
More than 100 Russian lorries entered on Friday without an Red Cross escort and most without customs clearance.
But Russia's President Vladimir Putin said further delays to the delivery of aid "were unacceptable".
Reports say the first trucks have reached the rebel-held city of Luhansk.
Reporters at the scene saw rebel fighters in front of the convoy as it crossed the border near the town of Kamensk-Shakhtinsky.
Ukraine's security chief Valentyn Nalyvaychenko said it was a "direct invasion" but no force would be used against the convoy as it wished to avoid "provocations".
The International Committee of the Red Cross (ICRC) said it was not part of the convoy "in any way".
Russia's foreign ministry has warned Ukraine not to take any action against the convoy, without specifying the consequences.
In a statement, President Poroshenko said "a column of more than 100 vehicles entered Ukrainian territory without a customs inspection, without border control or International Red Cross escort, which is a flagrant violation of international law".
Ukraine fears that the aid convoy of at least 260 lorries, which arrived at the border more than a week ago, is part of a broader Russian intervention in eastern Ukraine.
Russia denies accusations that it arms and trains the rebels in Luhansk and the neighbouring region of Donetsk, where four months of fighting have left more than 2,000 people dead and caused more than 330,000 people to flee their homes.