The resolution, passed by 140 “yes” votes, includes the majority of amendments put forward by the Ukrainian delegation, including a call to Russia to coordinate its humanitarian assistance to southeastern Ukraine with the Kiev government.
Earlier on Tuesday speaking at the PACE winter session in Strasbourg, Austria's delegate Johannes Hubner decried that the assembly's 47 members "missed the opportunity" to alleviate the Ukrainian conflict.
"Instead of this they tried to isolate one side and try to bargain or promote the military victory of another side," Hubner added.
The January 13 bus shelling in the town of Volnovakha in the Donetsk Region killed 13 civilians. At least eight Donetsk residents were killed in the shelling of a trolleybus stop last week.
Kiev forces and Donbas independence supporters have blamed each other for Saturday's shelling of Mariupol, a port city in southeastern Ukraine. The attack left 30 people dead and over 90 injured.
Kiev began a military operation on southeastern Ukraine in mid-April 2014, in response to the refusal by local residents to recognize a new coup-imposed government. The sides have repeatedly accused each other of violating a ceasefire agreement reached in September 2014 in the Belarusian capital of Minsk.