But a separate plan to set up animal welfare attorneys in an effort to improve animal rights failed to convince parliamentarians during a debate on Tuesday.
The House came out in favour of introducing mandatory third-party liability insurance coverage for dog owners.
Vets would have to report incidents with aggressive dogs, while owners would be required to put their canines on leashes when near schools and in public buildings, according to the proposed law.
However, parliamentarians stopped short of banning certain types of dogs considered dangerous.
More than 10,000 attacks by 200 different breeds are reported every year, according to the authorities.
The public controversy over dangerous dogs was triggered by a deadly attack by pitbulls on a six-year-old boy near Zurich in 2005.
In a related move, the House has discussed an initiative seeking to establish special attorneys acting on behalf of abused animals in court cases and criminal proceedings. Canton Zurich has pioneered such animal-welfare lawyers.
Supporters, notably the Green Party and the centre-left Social Democrats, argued the initiative would help enforce animal rights.
Opponents, including the centre-right Radical Party, the rightwing People’s Party, as well as the government, said a proposed regulation would infringe on the autonomy of the country’s 26 cantons.
Discussions are to continue on Thursday.
The Senate still has to discuss both issues before they come to nationwide votes at a later date.
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Each year, dogs bite around 13,000 people in Switzerland, resulting in serious injuries and even death. Zurich is voting on whether the most dangerous breeds, which have caused fatalities, should be banned. (SF/swissinfo)
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