The company has confirmed that about 50,000 more jobs may go, leaving the workforce at 100,000, compared with almost 250,000 a few years ago.
The disclosure by Sir Iain Vallance brought a furious reaction from the STE, which represents 22,000 managers.
Management grades are expected to be the main target in the the next round of job cuts, which will reduce the workforce by 15,000 this year alone. The rest are likely to be achieved within five years.
The union said members would be balloted for industrial action - which could include strikes - if there were any compulsory redundancies.
BT has said that it will attempt to make any cuts through voluntary means but admits that it might be difficult to achieve. About 90,000 jobs have been axed through voluntary severance in the past four years and unions question whether there can be thousands more willing to go.
Leslie Manasseh, national organiser, said: 'The problem is that the company has become obsessed with cutting staff costs. But when looking at the balance sheet overall, operational costs are still rising.'
Jeannie Drake, deputy general secretary of the National Communications Union, said: 'Reductions of this scale make no sense in commercial terms.' BT's quality of service and its ability to maintain the network would be impaired if the workforce shrank to 100,000.
In a joint statement, the BT unions said any threat of compulsory redundancies would seriously damage industrial relations.
'Over the past four years, BT unions have co-operated in reducing staffing by an unprecedented 90,000 jobs, while supporting the company's commitment to maintain the highest quality of service to customers.
'That co-operation was conditional on any job losses being voluntary and achieved through a combination of a voluntary release package and redeployment opportunities,' the statement said.
Part of the impetus for cuts is the tight regulatory regime under which BT operates. The company must keep within a price cap of inflation minus 7.5 percentage points. BT argues that this means it loses about pounds 500m in revenues every year, which it needs to balance by finding new business and reducing costs. The company's profits rose almost 40 per cent to pounds 2.7bn before tax last year.
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