But Frank Dobson, Secretary of State for Health, said the idea would have to be "looked at very carefully" before it could be implemented.
The report said that "non-medically trained staff" could be trained to do the job of anaesthetists under the supervision of doctors. So-called "nurse anaesthetists" already work in operating theatres in the United States and other European countries.
Mr Dobson said: "There's got to be the very basic test, we have got to make sure the patients are safe - that's got to be item one, two and three on the agenda."
Speaking on the BBC Radio 4 Today programme, he said he was "broadly sympathetic" to the idea of getting the best out of everyone working in the health service, and there were certain spheres in which nurses were keen to do more and the other professions were happy for them to do so.
But he warned: "It's something that needs to be looked at very very carefully because it wouldn't be in the interests of the patients to do something stupid and it wouldn't be the interests of nurses or the other professions.
"We have got to look at things very very carefully and see who can make a bigger contribution, who can relieve this problem of the shortage of anaesthetists which has been building up for five or six years."
The Audit Commission report said the biggest challenge facing doctors was the increasing number of patients needing treatment. "The most fundamental way to reduce demands for more doctors substantially would be to adopt the anaesthesia system used in many other countries in the world, including much of Europe and the United States - that is, allowing non-medically qualified staff to maintain anaesthesia under the indirect supervision of doctors, who move between two or more operating theatres."
Pilot schemes, using nurses to operate anaesthesia, should be introduced, the report said.