The NSW government is forging ahead with controversial plans to build a third cruise ship terminal in Sydney, despite strong opposition from residents and two local councils.

Transport Minister Andrew Constance and Tourism Minister Stuart Ayres are inviting the industry to provide input on a terminal at one of two potential sites on the northern side of Botany Bay.

Randwick City and Bayside councils are opposed to the idea of a cruise ship terminal at Botany Bay. Credit:Nick Moir

The Port Authority of NSW last month said staff had taken part in "informal discussions" with major cruise lines, including Royal Caribbean International.

Mr Constance said on Tuesday "this potential terminal at Port Botany" would address capacity constraints faced at the Overseas Passenger Terminal at Circular Quay.