The Ukrainian military said the rebels were pressing on with attacks on government forces near Mariupol, a port in government hands that is seen as the rebels' next major target.
Spokesman Andriy Lysenko said a military train carrying 60 armored vehicles including tanks had arrived in the town of Amvrosiivka from Russia on Saturday. A convoy of military equipment had later crossed the border near Novoazovsk, east of Mariupol on the Sea of Azov.
He said fighting was in progress at the village of Shyrokyne, east of Mariupol.
"The fight continues. Our soldiers are holding their positions," Lysenko said, adding that there had been a total of 44 attacks by separatists across the conflict zone in the past 24 hours.
In the city of Kharkiv, three people were killed and 10 wounded on Sunday when an explosive device was thrown from a car into a crowd attending a peace rally, a Ukrainian regional prosecutor said.
The blast, which police called a terrorist act, occurred near a metro station as a crowd of participants in the rally passed by.