After five hours of meetings, Bectu, the National Union of Journalists and Amicus rejected an offer tabled by the BBC.
The unions said the offer "had not gone far enough to avoid compulsory redundancies", although the BBC did promise a year-long moratorium on compulsory redundancies and pledged not to sell BBC Resources.
Bectu assistant general secretary Gerry Morrissey warned that further industrial action could still go ahead.
"There is still a significant gap between the unions and the BBC, which we hope will be bridged by divisional-level talks on the details of the cuts. If not, there will be renewed industrial action," he said.
The unions did, however, welcome the corporation's proposals on the delaying any sell-off of BBC Resources for two years and pension and benefits guarantees for staff at BBC Broadcast if it is sold off, as seems likely.
Last week, the BBC shortlisted four bidders for the sale of its BBC Broadcast business, including Apax Partners, where former director-general Greg Dyke is an adviser, and French manufacturing company Thomson/Technicolor.
Unions have now called for a meeting with director-general Thompson to discuss a framework in which negotiations on compulsory job cuts could go ahead without denying the unions the right to take further strike action.
If Thompson turned down a summit meeting, the unions said they would resume industrial action.
Jeremy Dear, the National Union of Journalists general secretary, said: "There is too much at stake for us to compromise the future of the BBC."
BBC staff agreed to call off yesterday's two-day strike action following 20 hours of talks at arbitration body Acas to resolve the dispute amicably.
If talks fail again it is unclear when the next wave of stikes would take place.
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