It is unclear when results of the recount, which includes votes cast in the presidential election, will be issued.
Police spokesman Wayne Bvudzijena told the state-controlled Herald newspaper petrol bombs were thrown at offices where ballot boxes for three constituencies in the Gutu rural district were stored early Friday morning, but all failed to explode.
ZANU-PF triggered the recount after it formally accused election officials of taking bribes to undercount votes for Mugabe and his ruling party and committing other electoral fraud. A number of election officials have been arrested since.
Harare's High Court rejected an MDC bid to block the recount on Friday. The court had previously denied its request to force authorities to release the result of the presidential vote.
Opponents accuse the 84-year-old Mugabe of wrecking this once-prosperous country, where the collapse of the economy and inflation of about 165,000 percent have led to chronic shortages of water, food and fuel, and 80 percent unemployment.
The delay in announcing results has given rise to opposition fears the recount could be a government ploy to steal the election.
"Clearly these guys have tampered with the boxes. They can't deny that," the MDC's Chamisa said. "How do you expect us to have confidence in the process?"
He said that in the Mberengwa West constituency, for example, the recount had been halted and paperwork including a copy of the voter roll were missing from the ballot box. He said some boxes from the Silobela constituency were not sealed.
Mugabe, in power since independence from Britain in 1980, has brushed aside criticism from London, Washington and opponents at home and is preparing for an expected run-off against Tsvangirai.
The MDC has accused the former guerrilla commander of unleashing loyal militias to help him rig victory in the runoff and allowing veterans of the independence war to invade some farms, echoing a wave of land invasions that began in 2000.
Human Rights Watch said on Saturday that ZANU-PF was using a network of informal detention centres to beat, torture, and intimidate opposition activists and ordinary Zimbabweans into voting for the ruling party.
On Friday, Mugabe said his government was only interested in peace and had intervened to stop war veterans from taking up arms.
