Ulster Unionist councillor Jim Rodgers said a preliminary ban on bus traffic was not enough.
It is almost a year since 16-year-old Ciara Park died after being struck by a bus at a busy junction in the heart of the city's shopping district.
Mr Rodgers said: "Ciara's death was unfortunately not the first serious incident in this area, yet we're still told it will be 2012 before all non-essential traffic is banned.
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"Piecemeal measures simply won't cut it - we need a big change before we face further deaths."
He claimed if the decision rested with the private sector the slow phasing of the scheme would progress faster.
"I know there is a lack of money in the public pot, but health and safety must come first. Money needs to be found so that this can be properly dealt with now.
"If this was a decision made in the private sector we certainly wouldn't be looking at an approach phased over a number of years."
Mr Rodgers suggested the phasing approach has caused confusion for the public.
"Plans for a one-way system along Royal Avenue must also be looked at. This area needs to be pedestrianised with only delivery vehicles allowed access during specific hours, such as 5am-7am.
"While there are various views on the pedestrianisation issue it is clear that unnecessary deaths must be avoided at all costs," he added.
(PR/GK)
