Moscow, at odds with Ukraine since pro-Western protests overthrew a pro-Russian president in February, had earlier expressed impatience with delays with the convoy, which left Moscow region around Aug. 13.
"We warn against any attempts to disrupt this purely humanitarian mission," the Russian foreign ministry said. "Responsibility for any possible consequences of provocations ... will lie, completely and entirely, with those who are prepared to further sacrifice human lives for the sake of their ambitions and geo-political ploys."
The International Committee of the Red Cross, which both Moscow and Kiev had agreed should supervise the convoy, said it was not escorting it "due to the volatile security situation".
The entry of the trucks ran counter to the arrangement agreed with the ICRC and was a clear violation of the border, Sebastien Brabant, spokesman for the European Union's foreign policy chief Catherine Ashton, said.
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NATO went a step further. "These developments are even more worrying as they coincide with a major escalation in Russian military involvement in eastern Ukraine since mid-August, including the use of Russian forces," Secretary General Anders Fogh Rasmussen said.
Kiev has been using troops, artillery and air power to try to quell a separatist rebellion that broke out soon after Russia annexed the Crimean peninsula from Ukraine in March.
The last few weeks has seen a string of rebel defeats in a conflict that has killed more than 2,000 people.
A Reuters cameraman said it had been possible to see inside some of the vehicles on Friday. The cargoes visible consisted of cardboard boxes with tinned food, pallets of bottled water, generators and other supplies.
Poroshenko said on Thursday he would call on Putin to rein in pro-Russian separatists when the two men meet next week and told the Kremlin chief he had "a strong country, a strong army".
Merkel is scheduled to visit Kiev on Saturday to show her support for Poroshenko - but diplomats say she is also bearing a message that he should consider calling a ceasefire so as not to incur a backlash from Putin.
In Donetsk, pro-Russia separatist Denis Pushilin, guarded by men who identified themselves as Chechens, handed out aid –sugar, tea, canned beef and rice – and envelopes of money to three families in a state building in the city center. The aid, collected in Russia by Russian citizens, was not connected to the aid crossing the border on Friday, Pushilin said.
"Hopefully soon we'll be able to start handing out aid to hundreds if not thousands of more families in need."
Rebels brought two destroyed Ukrainian armored personnel carriers to Donetsk's central Lenin Square to display on Sunday, when rebels plan on parading prisoners of war through the streets of the city as a counterpoint to festivities planned in Kiev as part of Ukraine's Independence Day.
After four months of fighting in the industrial, Russian-speaking east of Ukraine, the area faces a humanitarian crisis, lacking supplies of food, medicine and clean water.