Most Uber drivers named on an injunction application have indicated to their lawyer they will stop driving for the company until the matter is resolved.

Lawyers for the drivers and the City of Calgary appeared in justice chambers Friday morning, putting the matter over to Nov. 20 for a full day hearing on arguments for a temporary injunction.

Of the 57 drivers named on the application, Uber lawyer Christian Popowich said he represents 45 who have contacted him. He expects to hear from others in the coming days.

The city is trying to stop Uber from breaking bylaws by driving vehicles without proper insurance.

Uber has been telling drivers that their personal insurance provides primary coverage, while each ride is also covered by the company's contingent coverage up to $5 million for personal injury and property damage.

But the city says a driver's personal insurance is nullified when riders in private, unlicensed vehicles are charged.

The injunction being sought by the city says anyone who fails to comply to the terms of the order "may be arrested by officers of the Calgary Police Service and brought before this court to show why they should not be cited in contempt."

In April, the City of Edmonton also attempted to stop Uber drivers by seeking an injunction, but it was struck down.

The city is looking to amend its livery transportation bylaw to allow the app-based ride-hailing company to operate.