Unions have asked Transport Secretary Lord Adonis to intervene
There is "no reason" why the first national railway strike for 16 years should go ahead, Gordon Brown has said.
The RMT and the Transport Salaried Staffs' Association (TSSA) are planning four days of action from 6 April in a row over jobs and working practices.
The prime minister said the government "cannot tolerate large-scale industrial disputes" at a time when the UK was coming out of the recession.
But Tory leader David Cameron said Mr Brown needed to give "more of a lead".
Unions said they were available for talks to try to head off the action.
A spokesman for the RMT said: "We are drawing together a series of proposals which are aimed at resolving the issues at the heart of the dispute.
"That document will be submitted to Acas and once the various parties have had a chance to look at all the issues we will be getting back round the table for face to face talks with Network Rail."
The strike was announced on Thursday after a meeting between Network Rail and the RMT and TSSA failed to reach agreement.
TSSA supervisors and RMT maintenance workers are set to walk out from 6-9 April, while RMT signal staff will strike from 0600-1000 and 1800-2200 on those days.
At the heart of the row is anger at proposals to cut 1,500 jobs and changes which would see more work being done in the evenings and weekends.
The unions say the move would adversely affect railway safety - a claim disputed by Network Rail.
Mr Brown told reporters at an EU summit in Brussels that he hoped there would be no strike and that he believed no-one wanted to lose the threatened services.
He added: "Let me be absolutely clear, it is the public who come first. It is the citizens and consumers of this country who we work for and who demand, rightly so, that their needs are paramount.
"We cannot tolerate large-scale industrial disputes in this country, particularly at this time as the economy comes out of recession.
"There is a basis for arbitration of the rail dispute, that should be happening very soon and I see no reason why this dispute should go ahead."
However, Mr Cameron said the proposed rail strike, along with industrial action at British Airways and in the civil service, painted a "depressing picture".
"Strike action never helps, it never works and I think the government needs to give more of a lead.
"I think what we've heard from Gordon Brown has been rather mealy-mouthed, he couldn't even bring himself to say that he supported people who wanted to go back to work."
He added: "What sort of leadership is that when you've got strikes happening all over the country?"
Liberal Democrat transport spokesman Norman Baker said the RMT's claims about threats to safety on the railways were "scaremongering".
He added: "This strike is putting politics before the passenger and jeopardises future investment in the railways. The RMT are simply pulling the rug out from underneath its own members and passengers.
"Network Rail does need to be more efficient but this doesn't have to come at the cost of jobs."
There were fears that the strike would be called over Easter, but the unions said they deliberately avoided this in order not to disrupt the public over the bank holiday.
RMT general secretary Bob Crow said: "Despite long hours of talks, we have received nothing concrete from Network Rail that addresses the key issues."
TSSA general secretary Gerry Doherty said the strike was about "the safety of the travelling public and the safety and security of our members".
He urged Transport Secretary Lord Adonis to intervene.
Robin Gisby, Network Rail's director of operations and customer services, said: "Britain's railway is safer than ever. The issue of safety is a smokescreen from a union leadership stuck in the steam age.
"Our contingency plans are well advanced and aim to keep as many trains running as possible. But a national rail strike will have a severe impact on services and on Britain."
Network Rail said it hoped to achieve the "vast majority" of the 1,500 job losses through voluntary redundancy.
The Association of Train Operating Companies condemned the action, saying it would be "hugely frustrating for passengers and bad for British business".