Local government minister Kris Hopkins made the comment after the network warned that rural local authorities faced a worsening penalty because of the government's funding formula.
It comes as the government prepares to make a final decision later this month on local authority spending for the next financial year.
The network has calculated that a proposed settlement unveiled in December would see rural local authorities would be unfairly penalised.
The proposals would see local authorities in towns and cities receive £153 more funding per resident than rural authorities.
A vote on the Local Government Finance Settlement is expected to take place on announce its final finance settlement on Tuesday, 10 February.
The Rural Services Network, which includes 125 local authorities as members, has written to Prime Minister David Cameron ahead of the final decision.
The letter says a settlement which places an unfair burden on rural local authorities to implement further cuts will threaten the "long term viability of many rural communities."
It states: "When services are reduced or centralised in rural areas, people have to travel considerable distances to receive assistance and often the travelling involved and lack of public transport, means those services cannot actually be taken up."
Under the government's proposed settlement, a "sparsity" grant offered to rural local authorities will increase by £4m to £15.5m.
But the network has warned that spread over rural areas as a whole the additional grant could not possible deal with problems which were set to expand every year.
Mr Hopkins told the newspaper: "We are proposing to provide more funding this year, but we recognise there is still more to do."
Network director David Inman said: "The government has less than ten days to rectify the situation and we are asking that it puts things right."
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