City council has approved changing one part of the city's deal with the owners of the Calgary Flames to build a new hockey arena.

At a council meeting Tuesday night, councillors approved changing a single section of the city's deal with the Calgary Sports and Entertainment Corporation (CSEC) to replace the aging Saddledome.

The details were not made public, but the matter will be discussed again at a council meeting on July 5, said Mayor Naheed Nenshi.

He said the city is still negotiating with CSEC on the specifics of the contract section that's being altered, but he gave an assurance that it won't result in the city pouring in more money.

"Given materials cost, construction escalation, given some small changes to the program for the event centre, the costs have gone up," he said.

Nenshi said the start of construction, which was set for Aug. 1, is now likely to be delayed.

"Ultimately, we've got to figure out what we want to build here while staying in the context of the previous agreement that the city had made," he said.

"I still feel very confident that we'll be able to come to an agreement that Calgarians will support and we'll be able to build a facility that they can be proud of."

Nearly two years ago, council approved an agreement to split the cost of the $550 million arena in the southeast neighbourhood of Victoria Park.

The building would be the new home of the Flames and be an anchor for the planned entertainment district bordering the Stampede grounds on the east side of downtown. Preparation work on the arena was paused in April because of an unspecified budget issue.

Last week the Calgary Municipal Land Corporation (CMLC), the city-owned entity responsible for overseeing the project, said it is not involved in talks between the city and the owners of the Flames.