The Derby-based firm, which makes plane engines, said the reduction of nearly a fifth of its workforce would mainly affect its civil aerospace division.
“This is not a crisis of our making. But it is the crisis that we face and must deal with,” boss Warren East said.
The bulk of the job cuts are expected to be in the UK at its site in Derby.
Rolls-Royce employs 52,000 people globally and Mr East told the BBC’s Today programme that the company had not yet concluded on “exactly” where the job losses would be, due to having to consult with unions.
But he said: “It’s fair to say that of our civil aerospace business approximately two-thirds of the total employees are in the UK at the moment and that’s probably a good first proxy.”
Roll-Royce’s civil aerospace business has a number of sites in the UK, but the largest plant is in Derby.
Unite the union said the decision was “shameful opportunism”.
“This company has accepted public money to furlough thousands of workers,” said Unite’s assistant general secretary for manufacturing, Steve Turner.
“Unite and Britain’s taxpayers deserve a more responsible approach to a national emergency. We call upon Rolls-Royce to step back from the brink and work with us on a better way through this crisis.”
Rolls-Royce initially furloughed 4,000 workers in the UK last month. Some 3,700 people remain on the Coronavirus Job Retention Scheme though which the government pays 80% of a worker’s wage up to £2,500 a month.
But Mr East said: “No government can extend things like furlough schemes for years into the future. We have to look after ourselves and make sure we meet medium term demand.”
Air travel has ground to a virtual standstill since the coronavirus began spreading across the world and many airlines have announced steep job cuts.
Global air traffic is expected to decline by 45% this year, according to investment bank Baird. It also forecasts that airlines are expected to lose $310bn (£253bn) in revenue in 2020.
Rolls-Royce said the impact of the pandemic on the company and the whole of the aviation industry “is unprecedented”.
It added that it is “increasingly clear that activity in the commercial aerospace market will take several years to return to the levels seen just a few months ago”.
As well as the job losses, the company said it would cut costs in areas such as its plants and properties. It expects to make cost savings of £1.3bn.
Paul Everitt, chief executive of ADS, the aerospace industry association, said: “The crisis is having a major impact on aerospace companies who provide high value, long-term jobs in all regions and nations of the UK, putting thousands more jobs at risk now and in the months ahead.”