The two-minute video featured the dogs dying after apparently being injected with burning acid in an industrial area of Shiraz, 900 kilometres (530 miles) south of Tehran.
The Fars news agency quoted the animal welfare activist who filmed the undated footage as alleging that those responsible had been paid "$4 for the body of each dog".
Vice President Masoumeh Ebtekar, whose Tehran office was the venue for the biggest protest so far with 500 people on Sunday, criticised the killings and called for an investigation.
There should be "an immediate end to unconventional population control methods for stray dogs," she said in a letter to the interior ministry published by the official IRNA news agency on Monday.
She urged authorities to "deal with the criminals responsible".
Protests have taken place in Shiraz and other cities including Qazvin and Karaj, both west of Tehran.
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Dog ownership is controversial in Iran as Islamic custom regards the animals as unclean.
Some families do keep dogs as pets behind closed doors and, especially in more affluent areas, walk them outside.
A bill drawn up by hardline lawmakers last year would have outlawed dog ownership with offenders liable to up to 74 lashes.
State television showed Ebtekar addressing the protesters on Sunday at the environmental protection department she heads, telling them "municipalities, under the supervision of city councils," hold responsibility for pursuing the incident.
"Hurting animals is unacceptable under any circumstances," she told the crowd, according to the ISNA news agency.
Ali Karimi, a retired star of Iran's national football team who played for Bayern Munich, wrote alongside a picture of his two dogs on Instagram: "Dogs are the kindest domestic animals. I hope those who, under any excuse, did this to these animals get what they deserve."
The municipality of Shiraz was besieged by telephone calls from angry citizens after the footage surfaced last week, municipal official Jafar Omidi told Fars.