"Three fighters were killed and six wounded" in the village of Shyrokyne, the official rebel news agency said on its website.
The separatists accused government troops of flouting a truce signed last month by carrying out 33 attacks over the last 24 hours.
The attacks were mainly focused on Shyrokyne and the airport in the rebel bastion of Donetsk, according to the agency. Donetsk fell under separatist control in January after months of fierce fighting.
In accordance with the Minsk ceasefire deal signed last month, fighting has died down along most of the front line as both parties say they have withdrawn heavy arms to create a buffer zone ranging from 50 kilometres (30 miles) to 140 kilometres, depending on the range of the weapons.
Mariupol is the largest city still under government control in the conflict zone. Many Ukrainians fear the steel-making hub could be the target of a new rebel offensive as it would help form a land bridge between Russian-annexed Crimea and the border.
The village has sustained heavy damage, particularly the 700-metre (0.4 mile) "no man's land" that separates both sides, according to an AFP journalist.
Separatists claim to control around 30 per cent of the village, and a rebel commander said that fighting with artillery and tanks took place on a daily basis.
"The main road was supposed to be the neutral zone, but they (Ukrainians) bombard it constantly so you can't even attempt to approach it," the commander, named Igor, told AFP.
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