A spokesman for the mayor said funding alternatives for waterfront trams would be considered once negotiations between the agency and their Christchurch-based operator were complete.
"A tram service between Wynyard Quarter and Britomart is still planned as part of an integrated public transport network," he told the Herald.
Waterfront Auckland chief executive John Dalzell would not comment on his board's decision, saying that would be inappropriate while he was in discussions with the operator.
Agency chairman Sir Bob Harvey could not be reached to clarify a claim by a senior source in the organisation that the board had decided to pull the plug on funding for several reasons, not just poor patronage but also perceived difficulties in integrating the trams with redevelopment plans for Daldy St through the heart of Wynyard Quarter.
Mr Lee said the picture was "a little confusing" in the absence of clear information to the council from the waterfront agency.
"It's disappointing that Waterfront Auckland, who are in and out of the council requesting support on a regular basis, haven't taken the mayor and chair of transport into their confidence," he said.
"It's not clear to me what they are doing and why - it's not a very good way for Waterfront Auckland to carry out public business, which is of great interest to the people of Auckland.
"Any talk of suspending the service is extremely disappointing given Waterfront Auckland have had two years to get on with extending the tramway to Britomart, where it will have a meaningful public transport role rather than its present role as a novelty attraction."
Mr Lee said major transport constraints were emerging in Wynyard Quarter, where the ASB Bank wants to move 1500 employees this year to its new waterfront headquarters, but where some leaseholders were indicating they did not want too many buses rumbling through the precinct.
He feared the proposed tramway extension was falling victim to squabbling between rival council organisations Waterfront Auckland and Auckland Transport - of which he is one of two council-appointed directors - over who controlled Quay St and Te Wero wharf en route to Britomart.
Latest patronage figures for the trams were unavailable yesterday from Waterfront Auckland, but they suffered a serious slump after the Rugby World Cup, when monthly patronage fell from more than 15,000 passenger trips to below 2000 in March last year, before rising to 4664 in April. But Mr Lee said he understood patronage had grown this summer.
Waterfront trams
* Two electric trams, with 52 seats and 32 seats respectively.
* 1.5km circuit of Wynyard Quarter
* Cost: $8m to set up, operating loss of $139,000 in first eight months to April.