Military exercises involving some 1,300 personnel from 15 nations have begun in western Ukraine.
Some 200 U.S. soldiers are participating in the annual Rapid Trident exercises.
This year's drills come amid tension between Russia and NATO over the Ukraine crisis.
They do not involve the live firing of weapons, but they have brought U.S. ground troops to Ukraine for the first time since Russia's annexation of Crimea in March and the start of the conflict between Ukrainian forces and pro-Russian separatists in eastern Ukraine.
NATO says the exercise, which ends on September 26, will improve interoperability.
The exercise kicked off at a Ukrainian military base in Yavoriv, near the Polish border, on September 15.
Local officials in the rebel-controlled stronghold of Donetsk said that six people were killed on September 14, the bloodiest day since a cease-fire was signed 10 days ago.
It was not immediately clear whether those killed were civilians or rebel fighters.
The cease-fire started on September 5 and has been broadly holding despite sporadic violations which both sides blame on each other.
The deal was negotiated by envoys from Ukraine, Russia, the separatists and the OSCE.
But Aleksandr Zakharchenko, the Donetsk rebel leader who signed the September 5 agreement in Minsk, accused Ukrainian forces on September 15 of violating the truce repeatedly and said further negotiations with Ukraine made no "sense."
In Kyiv, military spokesman Andriy Lysenko said on the same day that there had been some deaths among Ukrainian troops over the weekend, although he did not provide details.
Lysenko said 73 soldiers had been freed in an exchange with the rebels.
A monitoring team from the Organization for Security and Cooperation in Europe (OSCE) said it was also shelled twice in the city on September 14, but none of its members had been injured.