Several DUP councillors were among those who voted in favour of the motion, which was put forward by the SDLP's council member John Dallat.
The move came after Environment Minister Arlene Foster revealed earlier this week that she is "of a mind to approve" a private application by developer and fellow DUP member Seymour Sweeney.
The move sparked Sinn Fein to call on the DUP to clarify its relationship with Mr Sweeney.
Ms Foster has dismissed claims that her decision was influenced by Mr Sweeney's membership of the party as "rubbish", while Mr Sweeney has said that while he is a member of the DUP, he has never given any money to the party.
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Ms Foster has also hinted that she may consider taking legal action.
Enterprise Trade and Investment Minister Nigel Dodds said earlier this week that the project would cost more than £21 million and said that it would not be a "prudent use of taxpayers' money" to proceed with the project, given Ms Foster's consideration of the private planning application.
Mr Dodds said that his department and Northern Ireland Tourist Board had only become involved as "a potential developer of last resort", because key stakeholders were "unable, over an extended period of time, to reach agreement".
More than £1 million had been spent on the project so far by the department.
The previous visitors' centre had burned down in April 2000.
Nearly 500,000 people visit the Causeway, known for its polygonal columns of layered basalt, every year. It is the only World Heritage Site in Northern Ireland.
(KMcA/SP)
