The network issued the warning after MPs slammed a proposed financial settlement for local authorities as unfair.
This is the amount campaigners say the government still owes rural local authorities after it agreed to alter its funding formula in 2012 and give greater weighting to sparsity.
Government ministers have proposed a much lower settlement.
Campaigners say it unfair that urban residents receive 45% more in central government grant than their rural counterparts – despite paying £81 less in council tax per head of population.
The impact of the balance is exacerbated because it costs more to deliver public services in rural areas.
A debate in the House of Commons, led by Rural Fair Share chairman Graham Stuart MP, saw a host of MPs speak out against the government proposals (click on video, right).
A crucial vote will take place on the settlement in February amid growing warnings that the funding gap between urban and rural areas must not be widened.
Network chief executive Graham Biggs said already cash-strapped local rural councils would face the prospect of being forced to increase council tax much more than urban councils.
Even then, they would still have to undertake swingeing service cuts, he said.
"The government must think again on this issue of fundamental unfairness."
Proposed changes to the funding formula had been applied unevenly and at the last minute by the government, said Mr Biggs.
Without any forewarning, they would have the effect of further penalising rural areas, he added.
The government has announced plans to increase the Rural Services Grant work for the most rural areas by an extra £20m in 2016-17.
But Mr Biggs said a promised extra £50m by 2019/20 over and above the £15.5m paid in 2015/16 was "back-end loaded".
The government had implied there was £20m extra funding in 2016/17 when, in fact it amounted to just a £4.5m increase to £20m compared to 2015/16.