The owners of dogs that attack and kill someone could face life in prison under new proposals for England and Wales.
The current maximum prison sentence for allowing a dog that kills or injures someone to be dangerously out of control is two years.
The government has proposed a number of sentencing options for a fatal dog attack - from five years to life. But the RSPCA said more needed to be done.
Sixteen people have been killed by dogs in the UK since 2005.
In March, 14-year-old Jade Anderson was killed in an attack by four dogs while she was at a friend's house near Wigan, in Greater Manchester.
Police have no plans to prosecute anyone in relation to her death, saying there is no evidence a crime has been committed under current laws.
At present, the Dangerous Dogs Act 1991 covers only attacks by dogs in public places and private areas where animals are prohibited from being, such as a neighbour's garden or a park.
A government consultation on the new proposals, which will run until 1 September, follows the announcement in February of plans to extend the scope of the law to enable a prosecution to be brought against anyone whose dog injures someone or acts aggressively in a private place where they are permitted to be, such as the owner's home.
Under the consultation, jail terms suggested for a dog owner whose animal injures a person or kills an assistance dog, like a guide dog for a visually impaired person, range from three years up to a maximum of 10.
The process will be used to inform recommendations put forward in the Anti-Social Behaviour, Crime and Policing Bill.
Animal Welfare Minister Lord de Mauley said: "Dog attacks are terrifying and we need harsh penalties to punish those who allow their dog to injure people while out of control.
"We're already toughening up laws to ensure that anyone who owns a dangerous dog can be brought to justice, regardless of where a dog attack takes place.
"It's crucial that the laws we have in place act as a deterrent to stop such horrific incidents."
But animal welfare charity the RSPCA said more should be done to stop attacks happening in the first place.
"Unless you solve this problem of people not being able to control their dogs properly then I still think you're going to see a rise in dog attacks and dog biting," said head of public affairs David Bowles.
He told BBC Radio 4's Today programme the government needed to give local councils the power to impose control notices and mandatory training on owners.
"What the government has proposed is only having a notice after the dog has committed the offence," he added.
Unions representing postal, utility and delivery staff have long argued for laws to be extended to cover attacks in dog owners' homes, saying this is a "major loophole" in the legislation.
According to the Communication Workers' Union, 23,000 postmen and women have been attacked by dogs in the last five years, with as many as 70% of these attacks taking place on private property.
Dave Joyce, the union's health and safety officer, said: "This consultation is very welcome and hopefully indicates the government is serious about tackling the problem of irresponsible dog ownership.
"We want to see tougher sentencing, better enforcement and greater consistency in sentencing.
"At the moment people are being handed vastly different sentences for very similar crimes, with one person receiving a suspended prison sentence while another walks away with just a £100 fine."
A spokesman for the Sentencing Council disputed the union's claim, saying new guidelines were brought in a year ago "to encourage consistency in sentencing".
A report published in June by charity Guide Dogs revealed that attacks by other dogs on guide dogs are at an all-time high of 10 a month.
Guide Dogs chief executive Richard Leaman said: "It's almost impossible to imagine the devastating effect an attack on a guide dog can have on someone with sight loss.
"The punishment for irresponsible dog owners should reflect the immense turmoil and anguish these attacks cause our guide dog owners, and all assistance dog owners. We are pleased the government is asking for views on this issue."
Last month, Jade Anderson's parents, along with the parents of four-year-old John Paul Massey who died after his uncle's pitbull attacked him in 2009, handed in at 10 Downing Street a petition calling for action to prevent similar attacks.
They called for preventative measures and education to put a stop to the 210,000 attacks and 6,000 hospital visits said to be caused by dangerous dogs each year.