Up to 6,000 people will be made redundant by August next year because of strike action and rising losses at the business.
The postal company said it had begun notifying workers of its plan, which will result in a reduction of 10,000 employees.
Most of the cuts will be made through redundant workers.
The full-year losses of Royal Mail are expected to be over a half a billion dollars.
The impact of the industrial action included lower volumes of parcels being posted.
If customers move volume away for longer periods, the firm warned, losses could reach as much as £450 million.
This is a sad day for the Royal Mail. These job losses are regrettable. We will do everything we can to avoid compulsory layoffs.
Fourteen thousand people are employed by the company.
Royal Mail workers, who are members of the Communication Workers Union, began a fresh round of strikes over pay and conditions which will include 19 days of industrial action.
Royal Mail's announcement is the result of mismanagement and a failed business agenda of ending daily deliveries, a wholesale levelling-down of the terms, pay and conditions of postal workers, and turning Royal Mail into a gig economy style.
On Friday, Mr Thompson said strike days weaken the financial situation.
The risk of more layoffs is increased by the CWU's decision to choose strike action over resolution.
Postal workers are being held to ransom for taking legal industrial action against a business approach that is not in the interests of workers, customers or the future of Royal Mail. It's not a way to build a company.
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