Cameron gives elected mayor views in Birmingham
Prime Minister David Cameron says the public will decide whether to have elected mayors but believes "great cities need great leaders".
In 2009, the Conservatives said if they won power, 12 of England's biggest cities outside London would get a vote on bringing in directly elected mayors.
In an interview with BBC Midlands Today, Mr Cameron said having such a mayor "helps a city to grow".
Plans for elected mayors have been suggested for Birmingham and Coventry.
Speaking to the BBC during the week of the Conservative Party conference in Birmingham, Mr Cameron said: "In the end it will be for the public to decide: 'Do you want to have city mayors?'
"My personal view is that...great cities need great leaders.
"Having someone to hold accountable for when they get it right or when they get it wrong actually helps a city to grow and to invest and succeed."
Birmingham City Council and Conservative group leader Mike Whitby has expressed reservations over the issue.
Asked if he would like to see Mr Whitby elected, Mr Cameron said: "I think he is a great leader and I think he'd make a great mayor.
"I think the council here is doing an excellent job in many regards."
The Tory proposals in 2009 would see a series of referendums held across 12 cities on a single day.
Birmingham, Bradford, Bristol, Coventry, Leeds, Leicester, Liverpool, Manchester, Newcastle-upon-Tyne, Nottingham, Sheffield and Wakefield could get mayors with similar powers to London's Boris Johnson.
Mr Cameron also defended high-speed rail plans in the interview with BBC Midlands Today.
The government will back plans for high-speed rail links to Manchester and Leeds, Transport Secretary Philip Hammond said.
'Huge economic benefits'
The planned new 250mph rail route between London and Birmingham aims to cut the journey time to 49 minutes.
But a protest was held near the Conservative Party conference on Monday against the proposed HS2 high-speed rail link involving the STOP HS2 group, which has expressed concerns over the environment and funding.
Mr Cameron said: "I think it's important as we make difficult decisions about spending public money that we do try and keep going with capital expenditure that will actually make our economy more productive for the very long term.
"If you go back over history, and you look at the big transport decisions, whether it is motorways or high-speed railways or channel tunnels, these can bring huge economic benefits to the regions of Britain."
Mr Cameron was also asked by the BBC over the fact Education Secretary Michael Gove had not yet visited Sandwell, after three pupils invited him to visit so he could assess the borough's need for new school buildings.
The members of Sandwell council's youth cabinet have written to Mr Gove asking him to view the nine school building projects he halted to save cash.
Sandwell was originally told none of its projects would be affected but the decision was later reversed.
Mr Cameron said: "I'm sure he will get there before long."