Asked whether he was seeking to cement the monarchy into Australian life, Mr Abbott said: "No, I'm not."
"Everyone knows where I stand on this particular issue," he said.
"I am a staunch supporter of our existing constitutional arrangements - always have been and, I imagine, always will be.
"But ... I think it is entirely appropriate that someone who represents the monarch should be honoured in this way."
Australian Republican Movement national director David Morris called it a retrograde step.
"This is turning the clock back to a colonial frame of mind that we have outgrown as a nation," he said.
Mr Morris also questioned why the current system was deemed insufficient.
"Our identity today is Australian, so our national honours should be thoroughly Australian."
The prime minister consulted Dame Quentin and General Cosgrove on the proposition and said they were happy to accept.
Shadow attorney-general Mark Dreyfus said the move showed the government was rushing back to the 19th century.
"Even the arch-monarchist John Howard didn't bring back knights and dames," Mr Dreyfus said.
Dame Quentin's son-in-law, Opposition Leader Bill Shorten, said the government had a plan for knights and dames but no plan for job creation.
"I'm concerned the Abbott government thinks this is a priority - what about jobs, health and education?"
Australian Greens leader Christine Milne said Australia had gone socially backwards under Mr Abbott's government.
"Bring on a republic," she said.
Palmer United Party leader Clive Palmer joked on Twitter that he probably would not be up for such an honour.
"Professor Sir Clive Frederick Living Treasure Titanic II Palmer sounds good but probably won't happen."
- AAP
