Royal Mail has offered to approach the conciliation service Acas to discuss modernisation, but only if union members call off planned strikes.
The Communication Workers Union (CWU) has called for independent mediation - backed by almost 100 MPs.
Talks between Royal Mail and the CWU aimed at avoiding strike action broke up on Monday without agreement.
The sides are thought to have little chance of reaching a deal before the first strike planned for Thursday.
In a separate development, the BBC has learned that the Ministry of Defence is making contingency plans to ensure that British troops in the field will get their Christmas post should the dispute not be resolved.
Under the plans, additional aircraft could be provided to move mail between Britain and Afghanistan and within the UK.
The talks between the two sides, held in Windsor, came after the CWU attacked Royal Mail's decision to hire up to 30,000 temporary workers as "a stupid move".
Management said the extra workers would cut the impact of "unjustified and irresponsible" industrial action.
The CWU has called nationwide 24-hour strikes on Thursday and Friday over pay, conditions and postal reforms.
EXPECTED STRIKE DISRUPTION
22 October: Limited processing, movement and collection of mail
23 October: Limited delivery and collection of mail
Some managerial staff and contract drivers will be brought in to move mail but services will be "very limited"
Special Delivery and Royal Mail Tracked items will still be delivered on strike days
Post Office branches will be open as usual although collections will be affected
Parcelforce will operate as normal as it has its own collection, distribution and delivery network
Customers should check the Royal Mail website or call 08457 740 740 for the latest service information
On Thursday, 22 October, mail centre staff and drivers will strike. The next day it will be delivery and collection staff.
Meanwhile, TNT, the UK's largest private mail firm, says it has an "alternative" plan for the future to be able to deliver mail directly to people's letterboxes - the so-called "final mile".
Royal Mail currently handles the final delivery of 99% of all letters under 350 grams.
TNT has carried out a trial run in Liverpool which has seen postmen in orange uniforms make door-to-door deliveries.
"We need the market and regulatory barriers moving before we can put orange postmen on the street," said Nick Wells, chief executive of TNT Mail UK.
"We have an alternative potentially for the future but not for the moment. Royal Mail has a de facto monopoly on the final mile delivery."
Royal Mail will be hiring double the 15,000 temporary staff it usually takes on before Christmas.
The extra workers will deal with the backlog caused by the strikes as well as helping with the Christmas rush.
Employing extra people to do the work of staff who are on strike is illegal under employment law.
Royal Mail said the recruitment drive was not about bringing in workers to do the work of striking staff, but to ensure there were enough staff to clear any backlogs between walkouts, as well as tackle the seasonal increase in mail volume.
CWU General Secretary Billy Hayes welcomed Lord Mandelson's suggestion of the use of the conciliation service Acas.
He stopped short of describing the extra temporary workers as strike-breakers.
He said: "What I'd sooner Royal Mail be doing is negotiating seriously about trying to find a resolution to this dispute."
But the government has warned the CWU to bear in mind that there are alternatives to the postal system.
"Technology is providing new ways of communicating," City minister Lord Myners said.
Liberal Democrat leader Nick Clegg told the BBC: "I think the people who are calling for a strike are wrong, which isn't to say they don't have legitimate concerns. But taking the whole country hostage like this is the wrong thing to do."
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