Labour's London mayoral candidate Ken Livingstone has described the position as an American concept which is "a bit alien".
He said it was always his fear that a mayor would be "focused on trivial personality politics".
Mr Livingstone made the comments at the launch of his manifesto, which was attended by Labour leader Ed Miliband.
It includes promises to cut transport fares, energy bills and rental costs, and to reintroduce the Education Maintenance Allowance for students in the capital.
He urged Londoners to use a calculator on his campaign website which shows "how they will be better off" with him as mayor.
Mr Miliband said his party's candidate has "always been the underdog" in the campaign, but had fought his way back into the race through "the power of his ideas".
The focus of Mr Livingstone's manifesto, unveiled in an event at Ravensbourne College in Greenwich, south-east London, is a commitment to cut transport fares by 7% this year.
He said it would be funded by Transport for London's "completely unacceptable" cash surplus, and would save the average Londoner £1,000 over four years.
He is pledging to reinstate a London Education Maintenance Allowance of up to £30 a week to help young people stay in education.
The manifesto also states that he would work to reduce rents and improve homes with a non-profit lettings agency, while "rip-off energy prices" would be cut by creating a co-operative.