MSPs on the Scottish Parliament's local government committee agreed that animal Asbos – anti-social behaviour orders – could improve the behaviour of both animals and their owners.
Their support, however, was qualified by doubts over whether councils would have enough cash to implement the plan.
The committee was considering a members' bill from Christine Grahame, the South of Scotland Nationalist MSP, which calls for the introduction of dog control notices.
These would allow councils to impose measures on dog owners if their pets displayed poor behaviour, which need not necessarily be classed as dangerous.
Pet owners could be forced to keep their dog on a lead in public, have the animal neutered, attend dog-control training courses and face fines of up to 1,000 if they failed to comply.
Over the past decade, the number of attacks by dogs in Scotland has risen from 239 to 623.
Scottish Borders Council has told MSPs it would need more cash from the Scottish Government to be able to implement the proposed Asbos.
And the National Dog Warden Association warned that "dog Asbos" could lead to a flood of complaints.
In their report on the proposal, MSPs on the local government committee said they agreed with Ms Grahame that current dog control laws were "piecemeal" and were focused on the breed of the animal and not its behaviour.
They backed the key aims of the Ms Grahame's bill: to promote more responsible ownership of dogs and to educate owners about their responsibilities.
While MSPs had "some concerns" about parts of the dog control notice regime, they said they believed that the proposed measures "should help to improve the behaviour of dog owners and that this in turn should lead to an improvement in the behaviour of their dogs".
However, the MSPs also raised concerns about the estimated cost of the proposals.
Papers lodged with the bill estimated a total cost to councils of issuing dog control notices to be just over 4,000 a year but MSPs said the Scottish Government had cautioned that the estimates "may be on the low side".
The committee called for Ms Grahame to respond to the concerns raised.
Committee convener Duncan McNeil said: "We welcome this bill that will ensure owners who allow their dogs to be out of control and a danger to the public are penalised.
"While the committee is in support of the bill, concerns were expressed that the costs to local authorities of implementing the dog control notice regime would be higher than envisaged.
"We have, therefore, asked Christine Grahame to respond to these concerns."
Ms Grahame has insisted that the cost of implementing her bill would be modest.
Last night, she said: "This is designed to be a preventative measure, so there should not be additional costs. This is not about dangerous dogs, it is about keeping them under control before they become dangerous. Local government is always complaining about extra costs.
"The legislation is to encourage responsible ownership and that will save court costs and hospital costs. Dogs do not start out as dangerous animals when they are puppies."