The conference has called on the Orange Order to "obey the rule of law by immediately disbanding the protest at Drumcree Church and following the alternative route laid down by the Parades Commission."
Supporting the resolution at the party's annual conference in Bangor, Co Down, on Saturday, Mr Tom Campbell, an Alliance party councillor in north Belfast, described the continuing protest at Drumcree as "farcical".
"The Orange Order must understand that it cannot cherry-pick the law, disobeying laws that don't suit them," he told delegates.
Mr Campbell called on the Church of Ireland, of which Drumcree is a parish, to use its influence to resolve the situation before the summer. "Many Church of Ireland clergy I have spoken to are deeply incensed at the situation," he added.
Addressing the conference during a panel discussion on policing and justice on Friday night, the Parades Commission chairman, Mr Alistair Graham, expressed concern about the continuing friction in Portadown.
"If we have to make a decision again on the Drumcree parade this year, the atmosphere in Portadown will make this an extremely difficult task. But let's be under no illusion - whatever decision we take it will not resolve the basic issue. Only the two communities coming together can do that."
Mr Graham said there could be "no excuse" for the picket of a Catholic church at Harryville, Ballymena, Co Antrim. "I have great difficulty understanding what is in the mind of people who prevent others from attending worship in an aggressive fashion. In fact, I cannot think of anything more intolerable."
Describing the parades issue as a "microcosm of our society", The RUC Chief Constable, Sir Ronnie Flanagan, another panel list, said it was quite wrong to compare a parade to attending regular worship. "There can be no legitimate linkage between the two," he said.
The Alliance Party spokesman on justice, Mr Steve McBride, praised the RUC for "an outstanding job in absurd circumstances" at Drumcree.