Mark Thompson has fleshed out plans for job cuts
The decision came after a three-hour meeting between unions and the BBC's director general, Mark Thompson.
Bectu, Amicus and the National Union of Journalists (NUJ) said the BBC had refused to meet their demand that there should be no compulsory redundancies.
The BBC said it regretted the decision by the unions, who also warned that strikes could hit live programmes.
Three years
The BBC said any action which affected services would penalise licence payers.
Luke Crawley, of Bectu, said the job losses represented the "most damaging cuts" in the BBC's history. He said under the plans up to 20% of staff jobs were being sold, outsourced or made redundant.
Mr Crawley added: "Our members want a BBC that works well, but Thompson's plans could stop some parts working at all."
Mr Thompson has announced proposals to axe the posts over the next three years.
'Substantial' cuts
The corporation said the director general had explained the three-year plan would put over £350 million back into programmes and most of the job losses would be achieved through staff turnover and voluntary redundancies, but it could not rule out compulsory redundancies.
The unions are not convinced there is a need for such large cuts and had demanded a three-month consultation period and a bar on compulsory redundancies.
The BBC first announced plans for substantial job cuts in December, and expanded on them last month.
Under the plans, more than 2,000 jobs are to go in programme making departments, such as news, drama and factual and learning, and another 1,700 would be cut in support areas.
Trades unions are to ballot members on strike action following the announcement of 4,000 job cuts at the British Broadcasting Corporation (BBC).

Formal notice of the strike ballot was sent to the public service broadcaster today by BECTU, the technicians' union, the manual workers' union Amicus and the National Union of Journalists (NUJ), after the Director General, Mark Thompson failed to rule out compulsory redundancies.

The job cuts announced last month, amounting to approximately 20% of the BBC's staff, are part of £355 million of savings that the BBC are making before the review of the broadcaster's royal charter by the Department of Culture, Media and Sport, which fund the BBC through the license fee. Further production jobs are being moved into the private sector.

Luke Crawly of BECTU said that it was unrealistic to expect 100% programme quality from 80% of staff. Ballot papers will be sent in seven days, with the aim of shutting down live broadcasting of sports events including the Wimbledon Tennis tournament and the Football Association Cup final.

The BBC's rival ITV is experiencing strike action over wages at production companies London Weekend Television (LWT), Yorkshire TV, Granada and 3sixtymedia, that has led to prerecording of shows and has forced ITV to borrow studios at the BBC's Television Centre.