As part of this work, the authority needs to demonstrate that residents, businesses and other organisations in rural areas would take up superfast broadband if it was available.
To do this, people in the Teesdale and Weardale areas are being asked to complete and return, a survey registering their interest in the service.
A number of drop-in sessions and meetings have also been organised for mid February, where people will be able to find out more superfast broadband and the survey.
Phil Jackman, Durham County Council's head of ICT services, said: "The Digital Durham programme is really picking up pace and superfast broadband is set to become a reality across the county.
"The more people who get behind this initiative, the more successful it will be. I would, therefore, urge people to support us where they can."
Council deputy leader councillor Alan Napier said: "This is very welcome news as we move forward in another challenging year.
"Local firms and households will be greatly encouraged by this further investment, which demonstrates that we are making progress even in these tough economic times.
"It will reinforce our county's strong credentials as a great place to live and do business.
"High-speed communications have never been more vital in order to succeed in an ever more competitive and connected world."
Don McClure, Durham County Council's corporate director of resources, said: "The commitment of the people of County Durham to improve council services has been remarkable.
They have already demonstrated their determination to ensure their communities receive access to services such as superfast broadband.
"We need their help again so that Durham County Council can make the best possible case to be successful in achieving extra funding from its Rural Community Broadband Funding Bid.
Durham County Council was already fully committed to the delivery of superfast broadband across the whole of County Durham.
Mr McClure said: "We also need the people of Teesdale and Weardale to complete and return their surveys to us, in order to support our bid."