"When you implement such an ambitious project, you have to balance the imperatives of delivering on a statutory requirement and people's sensitivities," information and broadcasting minister Manish Tewari said.
The ministry's top bureaucrat, Uday Kumar Varma, said the deadline has not been revised, but a "transition time" of about a fortnight has been given.
The ministry has asked multi-system operators - an intermediary between broadcasters and local cable operators - not to pull the plug just yet.
Low-income households are often the slowest to upgrade to a set-top box, which costs Rs. 799, excluding taxes.
The exercise is the second leg of a compulsory digital upgrade in towns with a population of more than one million.
In December 2011, the Parliament passed a bill to digitise the cable-television sector by 2014 to enable better visuals, more channels and more revenue for broadcasters.
The Capital has already completed the process.