The company insists it "thought carefully" about the impact on customers and its business before making the decision to hike the costs.
The increases will come into force on March 31 - two years after the last rise in stamp prices.
It comes after Royal Mail vigorously denied a Sky News story last year by City Editor Mark Kleinman that the firm's boss Moya Greene was paving the way for a stamp price rise.
Stephen Agar, Royal Mail's managing director of consumer and network access, said: "We understand nobody likes to pay more, especially in the current economic climate."
Royal Mail said under current rules, it could have increased second class stamps to 57p.
It pointed out its prices were among the best value in Europe, where the average price of posting a first class letter is 67p and 60p for second class.
In other price changes, the cost of a first class stamp for large letters weighing up to 100g will rise by 3p to 93p, while an equivalent second class stamp will go up by 4p to 73p.
A 60% share of Royal Mail was sold off last year, and ministers have faced continuing accusations they under-valued the business.
It recently emerged that banks estimated its value at £8.6bn when approached in the months before the eventual sale for £3.3bn.
Business Minister Michael Fallon revealed the higher and lower estimates of 21 different financial institutions, on an anonymous basis, in answers to written questions from MPs.
One bank estimated the value could be as low as £2.8bn.
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