The Ukrainian military said Tuesday that no "serious fighting" has taken place between government troops and militants in the country's eastern region since an attack Monday night.
"Since 11 p.m. Sep 22, no attack has been reported. Overall, we can say that the night passed quietly," Xinhua quoted Andrei Lysenko, spokesman for National Security and Defence Council, as saying in a media briefing.
Meanwhile, the Ukrainian ultra-nationalist group, the Right Sector, which fights alongside Ukrainian soldiers, said on its Facebook page that two of its fighters were killed in confrontation with insurgents Monday.
Civilian casualties have been reported in the area of fighting.
Donetsk's municipal council said that the previous night's shelling on a residential area of the city killed at least one person.
Last Saturday, a new agreement was signed between the Ukrainian government and the militants to accelerate the peace process in the eastern regions.
Under the framework of the ceasefire protocol, reached in the Belarusian capital city of Minsk, Kiev and the rebels agreed to halt their offensives and pull artillery and rocket-launchers about 40 km away from the combat area, creating a 30-km buffer zone.