The Glasgow-based company has been appointed by esure to provide inbound and outbound customer service calls for a further three years to 2015.
A spokesman for Response said the number of staff will vary according to the work involved. The employees will be based in esure's office in Glasgow.
Eddie McDonald, head of sales and operational strategy at esure, said the companies had enjoyed a successful partnership over the past five years.
Last month Response announced it had won a contract to handle customer service calls for energy giant ScottishPower. The company said it expected to create 300 jobs in Glasgow to service the contract.
It currently has about 1000 employees.
In March The Herald revealed Response had lost a huge contract to service satellite broadcaster Sky. The jobs of around 950 workers were transferred to HeroTSC, one of the suppliers chosen for the Sky contract.
In the accounts of Reponse (Building Rewarding Relationships) for the year to June 30, 2011, directors said the loss of the contract would significantly impact the revenue of the business but predicted it would continue to prosper.