The latest violence flared on Tuesday after Russia, Ukraine, France and Germany scrapped plans for a summit in Kazakhstan this week because of the failure to implement a four-month-old ceasefire agreement.
Ukrainian President Petro Poroshenko condemned the bus attack as an act that "chilled the heart" and blamed it on the forces of the separatist Donetsk and Luhansk People's Republics.
"These deaths are on the conscience of the DNR and LNR gangs and on those who stand behind them," he said, promising to sign a decree on Wednesday on more troops for the front.
But his comments aroused indignation on Wednesday among some Ukrainians seeking tougher action against the separatists.
"The terrorists fire on a bus with pensioners, kill children, shoot volunteers and torture them in cellars and we say simply that we are 'ready'," wrote Oksana Zinovieva, a spokeswoman for Kiev mayor Vitaly Klitshchko, on her Facebook page. "We have been trying to convert readiness into action for too long already."
The death toll in the attack rose to 12 with the death overnight of one of those wounded, police said.
A senior official from the Organization for Security and Cooperation in Europe (OSCE) called for maximum restraint from all sides in the Ukraine conflict, which has killed more than 4,700 people since last April.
"Over the past 24 hours the situation has significantly deteriorated, especially near the Donetsk airport," said Ertugrul Apakan, head of the OSCE's special monitoring mission.
The conflict between Ukrainian forces and pro-Russian rebels began soon after Russia annexed Crimea last March, creating the worst crisis in East-West relations since the Cold War. Western governments accuse Russia of backing the separatists but Moscow denies sending in troops.
Photographs showed the bus peppered by holes, as were seats inside it. A long trail of blood marked the road beside it near the town of Volnovakha.
A regional Ukrainian administration spokesman said the bus was attacked by rebels using Grad rocket launchers while it was carrying civilians through a government checkpoint.
Separatists denied responsibility and said the bus had been attacked by small arms fire rather than a missile or shell.
Reports from Donetsk on Tuesday said a significant part of the airport's control tower - already a wrecked hulk with cabling and concrete dangling from it after months of shelling - had been destroyed.
The Sergei Prokofiev airport complex, opened to great fanfare by the now ousted president Viktor Yanukovich to mark the Euro 2012 soccer championship, has gradually disintegrated under months of fire.
But although it has not functioned since the onset of hostilities last April, with its runways cratered by shell holes, the airport has symbolic value for both sides. Government forces have repelled repeated rebel attempts to dislodge them.