Areas in some Toronto parks have been turned into temporary dump sites during the civic workers strike. (Canadian Press)

The business of running the City of Toronto will go ahead, despite the 31-day strike by municipal workers.

Mayor David Miller said Wednesday that a special meeting of city council will be held Aug. 5 and 6 "to consider truly urgent business."

Miller said it is impossible to hold a normal council meeting because of the strike.

"Only truly urgent items" will be on the agenda, he said. The agenda will be sent to councillors within the next week.

Miller also announced that people who have paid for summer programs will be given refunds. He promised more information on the refunds will be released on Thursday.

Injunctions will also be sought to deal with two problem areas: Campbell Park, where the medical officer of health has issued an order for pest control spraying, and to clean up illegal dumping at Bluffer's Park.

According to Miller, pickets have posed a problem for carrying out the cleanups.

"We've been trying to spray Campbell Park since Sunday," but union pickets have prevented the pest control measure, said Miller.

Both the city's inside and outside workers walked off the job on June 22.

The about 24,000 civic workers include garbage collectors, clerks, water and sewer workers, and workers at city-run daycares.