Ukraine's President Petro Poroshenko has accused Russia of a "flagrant violation of international law" after Russian humanitarian aid 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.
Analysis: Daniel Sandford, BBC News, Moscow
The risk of the Russian aid convoy causing a further deterioration in relations with Ukraine is now very high. Because the International Committee of the Red Cross is not part of the convoy, the government in Kiev may choose not to recognise it as a humanitarian mission.
The lorries are currently being accompanied by pro-Russian gunmen. The Russian foreign ministry has already sent a clear warning that if the convoy is attacked, Moscow may take action.
Luhansk has been without running water, power and phone communications for 20 days as government forces besiege it.
Citing "heavy shelling overnight" in Luhansk, an ICRC spokesperson in Moscow said it had concluded that it had not "received the necessary security guarantees from the fighting parties to allow us to escort the convoy at this time".
Luhansk's official council reported on Friday that the dire situation in the city remained unchanged with no halt in the bombardment.
Russia had decided to act because of the "clear procrastination by Ukraine", Mr Putin had told Germany leader Angela Merkel, the Kremlin said in a statement (in Russian).
In a telephone call the two had also discussed "certain steps that Russia and Germany could undertake in order to contribute to the swift end to the fighting and the establishment of internal dialogue in Ukraine", it added.
Ukraine's prime minister said the move was Russia's attempt to distract the world from the fallout of down of the Malaysia Airlines flight MH17 last month.
It was shot down by Russian military specialists not by "drunken" separatists, Arseny Yatsenyuk said in briefing to journalists.
Both the European Union and Nato have condemned Russia's violation of Ukraine's border.
EU foreign affairs chief Catherine Ashton urged Russia to reverse its decision and Nato head Anders Fogh Rasmussen said it would "only deepen the crisis in the region, which Russia itself has created and continued to fuel".
According to the independent Organisation for Security and Co-operation (OSCE) observer mission, a total of 134 trucks, of which 34 have been inspected, had crossed over the border by 14:20 local time (11.20 GMT).
They were occupied by 12 "support vehicles", including an ambulance.
The Russian foreign ministry warned against any attempts to sabotage the "purely humanitarian mission", saying it had been prepared in an atmosphere of full transparency with Ukraine and the ICRC.
Foreign journalists were allowed to look into the Russian lorries earlier this week, and found they contained humanitarian supplies such as baby food and cereals.