Roseanna Cunningham, who was bitten on the face by a dachshund as a child, said "it is hard to make an argument against mandatory microchipping".
Glasgow Provan MSP Paul Martin led a member's debate at Holyrood on the effectiveness of dog controls and said the attack on eight-year-old Broagan McCuaig by two American bulldogs in his constituency in October reinforced the need for tougher laws.
First Minister Alex Salmond, who met Broagan's parents and other dog-attack victims last month, has launched a consultation and summit on responsible ownership, and listened to Mr Martin's arguments in a rare appearance at a member's debate.
Mr Martin, a Labour MSP, said the lack of compulsory microchipping and licensing suggests MSPs "are not serious about ensuring responsible dog ownership".
But SNP MSP Christine Grahame, convener of Holyrood's Justice Committee, said irresponsible owners will still flout the law and may try to remove the chips. He also said record-keeping may be difficult when dogs change hands.
Conservative justice spokeswoman Margaret Mitchell said breeders should be made to chip dogs rather than owners.
Mr Martin welcomed the First Minister's regard for dog attack victims and his focus on responsible ownership.
He said: "Thousands of incidents involving out-of-control dogs have been recorded over the last five years in Scotland and there has been a 17% increase in such incidents.
"A lack of compulsory microchipping, or any kind of mandatory licensing, suggests to me that we are not serious about ensuring responsible dog ownership."
Ms Cunningham said: "On a personal level, it's hard to make an argument against mandatory microchipping in the current circumstances.
"Compulsory microchipping could reinforce the responsibility an owner should have for their dog's well-being and we want to talk to people about the practicality and effectiveness of widespread microchipping of all dogs.
"The reintroduction of dog licensing would have to be done on a different basis than before, because it was ineffective before.
"It could be done in conjunction with mandatory microchipping - the two are not mutually exclusive - and I think those two things together would probably promote responsible dog ownership.
"I do think there ought to be some question of criteria for ownership which needs to be part of dog licensing to ensure that owners are suitable."
Ms Mitchell said: "It's important not to exaggerate the potential impact microchipping could have on ensuring responsible ownership.
"When licensing of dogs was mandatory, it is estimated that only 50% of owners held a license.
"Irresponsible owners will continue to be irresponsible, so it therefore makes sense for breeders to microchip the dogs they sell."
Mr Martin also called for a restricted breeds list but this was met with scepticism.
Mr Grahame, who was the principle author of the Control of Dogs Act 2010, said: "So many dogs involved are crossbreeds and a problem with the Dangerous Dogs Act was it gave four breeds of dog which were not the dogs doing these awful attacks.
"I am absolutely for universal microchipping but I have issues with it being mandatory.
"Will the bad owners who breed dogs as aggressive weapons to tear other dogs apart in dog baiting have their dogs microchipped? I don't think so.
"What would happen to people who have their dogs stolen for use in baiting? They can be removed using a wretched evil process. Who will update the records of the microchipping?
"The changing of hands of dogs is a difficult issue."
Ms Cunningham said: "I would caution on the listing of breeds.
"I understand why people raise it, but from personal experience the only time I have been bitten by a dog in my life, when I was a small child and bitten on the face, it was a dachshund. I'm pretty sure a dachshund would never be listed."