NATO said Russian troops had been firing artillery across the border and within Ukraine in a major escalation of military support for pro-Moscow rebels since mid-August, a defacto charge that Russia was waging war on its former Soviet neighbour.
Moscow, which has thousands of troops close to the Russian side of the border, warned against any attempt to "disrupt" what it said was a purely humanitarian operation; it did not say what action it might take if the Ukrainian military intervened.
The US Pentagon press secretary accused Russia of violating Ukraine's sovereignty.
"Russia must remove its vehicles and its personnel from the territory of Ukraine immediately. Failure to do so will result in additional costs and isolation," Rear Admiral John Kirby said in Washington.
The United States and European Union have already imposed economic sanctions on Moscow and the Kremlin has retaliated; NATO has deployed extra troops in member states bordering Russia, including the Baltic states and Poland.
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 let them pass to avoid "provocations".
Kiev called on international allies to unite in "a decisive condemnation of illegal and aggressive actions" by Russia.
Rasmussen also said Russia risked further international isolation, although Europe has been reluctant to step up sanctions due to trade ties and its use of Russian gas.
Russia denied breaching international law and the Kremlin said Russian President Vladimir Putin had told German Chancellor Angela Merkel in a telephone call Moscow could no longer wait for Kiev's green light to help people in distress.
Poroshenko said more than 100 trucks had crossed the border, of which only some had been checked earlier by Ukrainian officials inside Russian territory.
Other Ukrainian officials said only 34 or 35 of them had been properly checked.
But Ukrainian authorities said the convoy would pass through an area where the rebels were firing so its security could not be guaranteed.
Interfax news agency said later that the first trucks had reached rebel-held Luhansk.
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 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."
Red Cross declines to escort
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.
Rasmussen 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," he said.
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, after protesters toppled Kiev's pro-Russian president.
The last few weeks has seen a string of rebel defeats in a conflict that has killed over 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".