Russia has accused the US of wanting "complete dominance" after the arrival of 300 troops in Ukraine to train Ukrainian troops.
Speaking at an annual security conference in Moscow on Thursday, Sergei Shoigu, Russian defence minister, said the US had crossed all possible lines and the move "could not have failed" to trigger a reaction, Reuters news agency reported.
General Valery Gerasimov, chief of the general staff of the Russian armed forces, told the audience at the same meeting that the US was trying to: "reshape the world to fit its needs".
"Aiming at complete dominance, Washington stopped taking into account the interests of other countries and respect international law," he said.
Troops from the 173rd Airborne Brigade arrived on Tuesday and Wednesday in Yavoriv, western Ukraine, to spend six months training three battalions of Ukrainian troops.
Tensions have been high between Russia and the US since former Ukrainian President Viktor Yanukovych was toppled after protests and fled to Russia.
The US and other Western countries accuses Russia of arming pro-Russian separatists who have taken control of some areas in eastern Ukraine, a charge that Russia denies.
The US troops will train the National Guard of Ukraine (NGU), a reservist force reformed in 2014 to bring volunteers and militia under government control.
"We will be conducting classes on war-fighting functions, as well as training to sustain and increase the professionalism and proficiency of military staffs," a US official said, according to the AFP news agency.
Fighting between the separatists and Ukrainian troops is rumbling on in the east despite a February ceasefire agreement.
The conflict has so far claimed more than 6,000 lives, according to the UN.
On Thursday a journalist known for his pro-Russia views was gunned down in Kiev.