Supporters of the measure held a rally in the city centre on Sunday.
A pack of dogs attacked the boy near a park a week ago. The city is reckoned to have about 65,000 stray dogs.
Campaigners in the animal rights group 4Pfoten (Four Paws) are urging the authorities to adopt mass sterilisation of dogs as the solution, instead of a cull.
The group’s campaign director Gabriel Paun told the BBC that 4Pfoten was castrating stray dogs in Bucharest, but that a much bigger effort was needed nationally to have an impact on the dog population.
“In the last few years we’ve castrated 100,000 dogs in Romania altogether, 10,600 of them in Bucharest, But it’s not enough, this is a voluntary private project – we need them to do the same thing at national level,” he said.
“It’s not a local problem, it’s national – even if Bucharest is free of strays, the dogs don’t have administrative borders – they will come back.”
Animal welfare officials say about 1,100 people were bitten by stray dogs in Bucharest in the first four months of this year.
President Traian Basescu has called on the government to pass a law on euthanasia for strays, saying “humans are above dogs”.
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