The GMB Union says Uber has been granted a six month extension to its licence in Brighton.
Discussions were held by the council on Tuesday, behind closed doors.
It is to allow the council to monitor Transport for London's decision about the company's operation in the capital.
The council will consider whether information arising from the case will have direct implications for its operation in Brighton.
It also allows more time for negotiations with Uber about a number of proposed conditions.
Uber allows users to book a journey and pay for it through a mobile app.
The company argues it has brought cheaper fares and faster response times for passengers.
But local taxi drivers in Brighton say it is unfair competition.
Under national law, licensed drivers can operate anywhere in the country, allowing drivers from elsewhere to work in the city.
All Brighton & Hove private hire and Hackney Carriage drivers operate under the same licences and the same guidelines as Uber drivers.
They are also bound by the same background checks.
For years, ever since they were pulled by horses, in fact, if you wanted a cab you stood on a street and hailed the driver. And that's still the way it works in many places. But there's a new kid in town. Uber.
It allows customers to use a mobile phone app to get hold of the nearest cab. Uber are often cheaper, but not everyone's happy - not least the drivers of the regular taxis themselves.
And now, the battle that has been fought in cities around the world is heading to Brighton.
Andy Dickenson reports. He speaks to Andy Peters from the GNB, John Streeter of Streamline Taxis, and Jason Kitcat of Crunch accounting.
The Uber mobile phone app allows customers or passengers to book a taxi from the firm and pay for it using their phone.
The drivers called partner-drivers are all self employed. According to its website Uber operates in 60 countries. It is already in use in London, Leeds, Manchester, Bristol and Birmingham and now it has applied for a licence in Brighton and Hove.
Brighton & Hove's city council has been given more time to make its decision. Local taxi drivers are concerned - they say that if Uber is granted a licence its drivers should be subject to the same rules and guidelines that they have to observe. Uber says it does abide by the rules.
The row centres around whether the increased competition for fares will be fair, whether background checks will be as stringent as for taxi drivers and whether Uber private hire drivers will have to / will be able to provide vehicles accessible for specific groups of the community, such as people who use wheelchairs.
Councillors in Brighton and Hove have been given more time to decide whether the controversial taxi app 'Uber' can be used in Brighton.
A meeting had to be adjourned yesterday - with cab companies already operating in the city arguing that the new service must face the same licence restrictions that they do. John Streeter from Streamline Taxis in the city gave us his view.