Moscow, which has thousands of troops close to the Russian side of the border, warned against any attempt to disrupt the convoy which it said was a purely humanitarian operation but did not say what action it might take if Kiev's military intervened.
Ukrainian President Petro Poroshenko described the entry of the trucks without Kiev's permission as a "flagrant violation of international law."
But a senior security chief said Ukrainian forces would not attack the trucks, and had allowed them in, even without proper clearance, to avoid "provocations".
The Ukraine conflict has driven relations between Moscow and the West to their lowest level since the Cold War, with Western states imposing economic sanctions on Moscow and the Kremlin retaliating. NATO has deployed extra troops in member states bordering Russia, including the Baltic states and Poland.
Kiev called on international allies to unite in "a decisive condemnation of illegal and aggressive actions" by Russia.
Mr Poroshenko said more than 100 trucks had crossed the border, of which only some had been checked earlier by Ukrainian officials inside Russian territory.
Repeating earlier suspicions by Kiev that the aid cargo could be somehow used to support the separatists, the foreign ministry said: "Neither the Ukrainian side nor the International Committee of the Red Cross knows the content of the trucks. This arouses special concern."
The fact Russian vehicles had crossed into Ukraine without permission "testifies to the deliberate and aggressive character of actions by the Russian side," the ministry statement said.
Ukrainian state security chief Valentyn Nalivaychenko said: "We consider this a direct invasion by Russia of Ukraine."
The largely Russian-speaking Donetsk and Luhansk regions both declared independence after a plebiscite deemed illegal by Kiev.
The regions have seen intense fighting in recent weeks as rebels have been driven back into pockets.
Moscow, which denies accusations it has given military support to the rebellion, had earlier expressed impatience with delays with the convoy which left Moscow earlier this month.
"All excuses to delay sending aid have been exhausted," the Russian foreign ministry said.
"We warn against any attempts to disrupt this purely humanitarian mission. 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 for 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".
Kiev has been using troops, artillery and air power in an attempt to quell a separatist rebellion that broke out soon after Russia annexed the Crimean peninsula from Ukraine in March.