Clifford Clarke, 79, was attacked in the back garden of his home Saturday evening, the Liverpool Echo reported. In a statement Monday, police said the women, ages 27 and 28, had been arrested on suspicion of manslaughter and a violation of the Dangerous Dogs Act.
They were granted conditional bail.
A neighbor described Clarke as a "lovely sweet old man." He said Clarke opened the back door because his kitchen had become full of cooking smoke.
Police killed the dog, describing it as "out of control." Investigators have not identified the breed, although one local resident described it as a "pit bull type."
Clarke's family called for stronger laws against dangerous dogs.
"He did not deserve this so please put your support behind new laws for dog owners because you would not like any of your loved ones to have this happen to them," his younger brother, Kenny, said.
A string of recent fatal attacks occurring on private property by legally owned animals have raised awareness on the issue, The Guardian reported. In March, after a 14-year-old girl, Jade Anderson, was killed by four dogs at a friend's house Greater Manchester police said the owner could not be prosecuted.
There were two attacks in November. A week-old boy was fatally injured by his family's Jack Russell terrier, and a woman was killed by her daughter's five dogs as she fed them in London.