Garvaghy Residents Coalition spokesman Breandan MacCionnaith said the order's proposal to march on 2 July would heighten tension in the area over a longer period.
The BBC's Jon Brain in Baghdad says the ambush happened during a night of tension in the area, as US troops continued their investigation into Thursday's bombing.
The Archbishop of the Roman Catholic Church in Bangladesh, Michael Rosario, said they had not received any threats and there was no report of any communal tension in that area.