KIEV -- 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 on Monday night.

"Since 11 p.m. local time (2000 GMT) on Sept., no attack has been reported. Overall, we can say that the night passed quietly," Andrei Lysenko, spokesman for National Security and Defense Council told a media briefing.

Meanwhile, the Ukrainian ultra-nationalist group, the Right Sector, which fights alongside with Ukrainian soldiers, said on its Facebook page that two of its fighters were killed in confrontation with insurgents on Monday.

Civilian casualties have been also 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 agree to halt their offensives and pull artillery and rocket-launchers about 40 km away from the combat area, creating a 30-km buffer zone.

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