The warning came as President Bill Clinton appealed on the eve of the first anniversary of the Omagh bombing for a permanent end to the culture of violence in the province.
Up to 10,000 bandsmen and members of the loyal order are due to attend the Derry march.
But as a major security operation began to keep the rival sides apart, police said that republican extremists had seized control of the Bogside protest.
RUC Assistant Chief Constable Alan McQuillan, who will have up to 1,000 police and troops available, said: "It is a bleak picture, which I hope will not be fulfilled. I hope it can be avoided."
Mr McQuillan said: "I have no doubt whatsoever, based on intelligence which is confirmed by information from community leaders, that extremists intend to orchestrate widespread violence, including the use of petrol bombs. Some of these have been stockpiled and supplies are being added to." If the extremists get their way, he warned, "the decent law abiding people of the city could once again find their streets strewn with burnt- out vehicles, shops and offices subjected to firebombing and people put at risk of maiming or death".
The Northern Ireland Parades Commission last night issued a statement saying that the nationalist protest was deliberately intended to clash with the Apprentice Boys march. "It will heighten tensions and could lead to a serious public disorder involving thousands of protesters," it said.
Even without the official restrictions, security chiefs in the city fear major trouble. The tension surrounding this year's march is further heightened by the significance of this weekend to republicans. Tomorrow is the thirtieth anniversary of Harold Wilson's deployment of British troops to deal with widespread disturbances in Belfast and Londonderry.
Designed as a short operation to restore peace and order, the military instead has become a permanent feature of Irish life. During the past three decades more than 200,000 soldiers have done tours of duty in Northern Ireland; 500 troops have been killed and about 300 people have been killed by them, including IRA members. The most controversial army shooting still remains that of 14 people on Bloody Sunday in Londonderry, 1972.