Yatseniuk, speaking in Odessa, attacked police forces in the Black Sea port city, suggesting they were more interested in the fruits of corruption than maintaining order.
Had they done their job, he said, "these terrorist organisations would have been foiled".
Friday's clashes were the most deadly since Moscow-oriented president Viktor Yanukovich was forced to flee in February and pro-Russian militants launched uprisings in the industrial east.
They also marked the first serious disorder outside eastern areas since Yanukovich fell, heralding possible future trouble for Kiev.
"There were dozens of casualties resulting from a well-prepared and organised action against people, against Ukraine and against Odessa," Yatseniuk said.
He dismissed Russian accusations that his government was provoking bloodshed in the east with an operation to restore Kiev's authority in a string of cities under rebel control.
"The process of dialogue had begun, only it was drowned out by the sound of shooting from automatic rifles of Russian production," he said.
The former Soviet republic of Ukraine is divided between a largely Russian-speaking population in the industrial east and Ukrainian-speaking west, where more pro-European Union views prevail. Moscow says Russian-speakers face threats from Ukrainian nationalist militants, an accusation Kiev denies.
Odessa was quiet yesterday. Flowers were laid outside the burnt-out stone building of a trade union organisation, which is now guarded by police, where the deaths occurred.
On social networking sites, pro-Russian activists called for a gathering on the "Kulikovo Field", a large square that was the focus of Friday's fighting.
The deaths occurred after running clashes, involving petrol bombs and gunfire, between supporters and opponents of Moscow on the streets of Odessa, which has a mixed population of Russian and Ukrainian speakers. The dead activists had taken shelter in the building.
Shooting was reported yesterday on the road between the eastern towns of Kharkiv and Izyum where Ukrainian forces took over a checkpoint. There were no signs of Ukrainian forces pushing their declared campaign to remove separatists from eastern cities including Kramatorsk, Donetsk and the rebel stronghold of Slaviansk.
Kiev is organising national elections for May 25.
However, as things stand, it would have trouble conducting the vote in many parts of the east, a circumstance that would allow Russia to declare any government emerging from the elections as bereft of legitimacy.
Russia denies ambitions to seize eastern Ukraine in the same way that it has annexed the Crimean peninsula, but reserves the right to send troops to defend Russian-speakers if it deems necessary.
Separatists who have declared a "People's Republic of Donetsk" are planning a referendum on secession on May 11.