It won 15 seats on five provincial assemblies, including eight seats in the important Western Province (which includes Colombo), where it holds the balanceof power in the assembly.
However, Mr Paisley has predicted that the DUP will hold the balanceof unionist power in the assembly and that his party will therefore have the power to block any such move.
Before the debate, Welsh Secretary Ron Davies made an impassioned plea to the conference not to tear itself apart in arguing over the mechanics of achieving gender balance in the assembly.