Kabul radio acknowledged that some districts had fallen but said forces loyal to the Government remained in control.
The Kabul radio in Afghanistan's capital reported that five people had died in the quake.
No reliable estimate of the number of dead was available; the official Kabul radio said "tens of people" had been killed.
The Kabul radio said the 53 dead included the members of the crew, 16 children and 10 women.
The Government-controlled Kabul radio said the rockets caused casualties in several parts of the city overnight and during the day.
The Government-run Kabul radio blamed a "small terrorist group" for the shooting.
The Kabul radio said recently that 417 "armed opposition groups" representing 37,000 people were "engaged in negotiations" on sharing power.
Najibullah, the Afghan leader, described the move as a step toward national reconciliation in the seven-year-old war, the Kabul radio reported.
No further details on the cease-fire were provided by the Kabul radio or by the Tass report.
Tass gave no explanation for the Afghan decision and the Kabul radio appears to have said nothing about it.