It said it was due to begin consultations with the Communication Workers Union and Unite over the move which will largely involve managerial positions.
The company, which controversially floated on the Stock Exchange last year, said that 300 new or enhanced positions would also be created, leaving a net reduction of 1,300 roles.
Royal Mail said the move would not affect postmen and women or the services provided to customers.
It said the proposed job losses were part of a cost-cutting programme to deliver annual savings of around £50 million a year, including £25 million in 2014/15.
The programme will result in an additional £100 million costs for the current financial year, taking the total to £230 million.
Royal Mail said it was committed to handling the consultation "carefully and sensitively". Its European parcel delivery company, GLS, is not affected.
It said that, since 2003, 50,000 employees had left the group and it had a strong record of "achieving change through natural turnover, redeployment and voluntary redundancy wherever possible".
Chief executive Moya Greene said: "We are continuously improving our efficiency, whilst maintaining our high quality of service.
"We need to do so in order to effectively compete in the letters and parcels markets. This is the best way to ensure the continued delivery of the universal service and the good-quality jobs we provide for our people."
The Unite union's Royal Mail officer Brian Scott raised the spectre of strike action in the event of compulsory redundancies
He said: "First the Government sells off Royal Mail on the cheap and now the newly privatised service is ruthlessly sacrificing jobs.
"We do not believe that it's a coincidence that this announcement has been made just before the company prepares to announce its first full set of accounts since privatisation.
"It's more proof that Royal Mail's primary reason for existing is now about making profits rather than serving the nation.
"For all that Royal Mail managers have been through they do not deserve to be treated in this way.
"Unite is demanding a commitment to no compulsory redundancies on fair terms and an effective method for redeployment within the restructured organisation. If Royal Mail refuse, we will have no alternative than to consider a ballot for industrial action."
The announcement comes just three months after Royal Mail struck an agreement with union leaders on pay, pensions and other issues linked to the privatisation.
Under the deal between the CWU and the company, which averted strikes, more than 130,000 employees would receive a three-year pay rise worth around 9% and legally-binding employment protections.
But there has been controversy over the salary of Ms Greene, amid recent reports that Business Secretary Vince Cable wants to block any rise of more than 3% for the chief executive. The Government still owns a substantial chunk of the company.
Labour has accused the Government of a "botched privatisation" of Royal Mail, saying taxpayers have been short-changed by hundreds of millions of pounds.
The market value of the company soared on privatisation last October, when shares were valued at 330p, though Mr Cable dismissed the steep rise when they began trading as "froth".
However, they have remained well above £5, helping the company enter the FTSE 100 index of top London-listed companies by valuation. Last night they closed at 584p.