The whole of Bristol could eventually see a 20mph speed limit.
A pilot zone was introduced in parts of the south of the city earlier, aimed at improving safety and encouraging people to walk and cycle.
Asked on BBC Radio Bristol whether all the city could see the limit, Councillor Jon Rogers said: "I think that would be what we would try to do.
"Obviously there's the cost... but the message we're getting from right across Bristol is that 20mph is enough."
Mr Rogers, the council's executive member for transport and sustainability, said the council would have to find the money, which was limited.
He said: "The message we are getting is people feel 20mph is quite fast enough where people live so why not?"
The pilot project has been developed as part of the Cycling City project, in partnership with Active Bristol.
A consultation into a 20mph pilot in east Bristol ends on Monday.