Union leaders are to meet BBC director general Mark Thompson for further talks next week aimed at averting further strike action at the corporation.
The first 24-hour strike disrupted output, particularly news
Mr Thompson, who is planning to cut 4,000 jobs, has said an offer to freeze compulsory redundancies until July 2006 was final.
The BBC's boss added the talks were being held to "clarify any queries".
Plans for a 48-hour stoppage on Tuesday and Wednesday were suspended after 20 hours of negotiations last week.
The BBC offered a one-year moratorium on compulsory redundancies and a delay to privatisation of some facilities.
But on Tuesday unions dismissed the offer as "not good enough".
Jeremy Dear, general secretary of the NUJ, warned that unions were prepared to launch fresh strikes and will not require another ballot.
The union had put the offer to Tuesday's meeting of union representatives as a gesture of goodwill, Mr Dear said.
But it had been rejected for the "very good reason" that it did not address the "disastrous impact" the job losses would have on programme quality and the health and safety of staff, he added.
"The management would be well advised to seriously reconsider these cuts if they want to avoid more disruption," he said.
The unions staged a one-day strike on 23 May over the corporation's plans to save £355m a year, which include the job cuts.
The BBC said 38% of staff due to work had joined the walkout, while the unions said they believed up to 55% had taken part.