The new channel forms part of the government's review of media and communications, unveiled by Hunt at the Oxford Media Convention.
Outlining a Local Media Action Plan from the Department for Culture Media and Sport (DCMS), Hunt said the initiative would offer communities a "new voice" and provide local perspectives directly relevant to them.
The initial schemes will be focused on 10 to 20 local TV services, operating by 2015 with the first local services licensed from 2012.
Hunt today called on media providers to register an interest in running the network channel by 1 March and market players to come forward with responses to a consultation on the plans and how best to provide services by 13 April.
"One way this could be provided is through sharing services, organising resources and sourcing network content which could be shown across the country when the local TV service is not being shown," the DCMS plan from the says.
"Another is combining local content with network content in individual locations tailored for those localities. The right capacity option becomes an important consideration here."
The DCMS plan builds on recommendations made by by Nicholas Shott in the Shott report, commissioned by Hunt last year.
The Shott report recommended that local television stations should be set up in 10-12 city areas, but Hunt said today the government would not be prescriptive about the number of areas around the country that will be involved.
"The eventual aim for local TV is that it is made available throughout the UK, providing local and relevant content to all who want to access it," the DCMS plan says.
"However, given the commercial uncertainty involved in relation to acquiring capacity and developing a sustainable revenue proposition, it is clear that local TV cannot simply be launched across the UK immediately."
Following the BBC licence fee settlement, the government has agreed that the BBC will provide start-up costs of up to £25m in 2013/14 for up to 20 local TV services, the Action Plan adds, and up to £5m per annum of ongoing funding from 2014/15 for three years to acquire content for BBC use.