The action, announced by Bectu, the National Union of Journalists (NUJ) and Unite, was planned to resume on October 19/20 when Chancellor George Osborne is to unveil details of spending cuts during the Comprehensive Spending Review.
But unions said they had received a "significantly improved" offer on pensions.
Gerry Morrissey, general secretary of the broadcasting workers' union Bectu, said that an improved offer will now be put to a ballot of members.
Next week's strike has been called off, but there is the threat of industrial action later in the month if the deal is rejected.
Mr Morrissey said a strike planned for October 19 and 20 would remain until the ballot result was known, and unions had decided to add another strike date of October 25 and 26.
Mr Morrissey said: "We have had a significantly improved offer from the BBC which we believe is the best that can be achieved through negotiation. If it is accepted, all the action will be called off, but if it is rejected, strikes will take place. We welcome the movement from the BBC."
The strike call came after a BBC announcement of plans to cap pensionable pay at 1% from next April and revalue pensions at a lower level, which unions said effectively devalued pensions already earned.
BBC management said the changes were needed to try to tackle a huge pension deficit of more than £1.5 billion.
Earlier, Ed Miliband, the Labour party leader, had called on BBC staff not to black out David Cameron's party conference speech by going on strike next week.
He said in the ''interests of impartiality and fairness'' the Prime Minister's speech should be broadcast on television and radio.
His call follows warnings that staff risk giving the ''misleading impression'' that they are not impartial if they strike during the Conservative Party conference.
Mr Miliband said: ''Whatever the rights and wrongs of the dispute between (broadcasting union) Bectu and the BBC, they should not be blacking out the Prime Minister's speech.
''My speech was seen and heard on the BBC and in the interests of impartiality and fairness, so the Prime Minister's should be.''
Mr Miliband narrowly beat his elder brother David in the race for the Labour leadership due to the support of the unions.
His statement will be seen as an early signal that he does not believe that he is in hock to them politically.
Mark Thompson, BBC director-general, had told staff: "Impartiality is the watch word and we do not want to give the misleading impression that this is no longer something we value highly. To be clear, this is not a comment on the principle of strike action.
"There are two questions I'd urge staff to think about: is this the right moment to strike, are these the right days? These are questions for individual staff to consider in the coming days."
Some of the BBC's most prominent presenters also warned over the timing of the strikes in a letter.
The letter, signed by Newsnight presenter Jeremy Paxman and BBC Political Editor Nick Robinson among others, said the move "risks looking unduly partisan".
Last month, Conservative Party chairman Baroness Warsi wrote to Mr Thompson asking for reassurances that the planned strikes would not breach impartiality rules by blacking out the conference.
Source:-
http://www.telegraph.co.uk/culture/tvandradio/bbc/8037461/BBC-strike-called-off-...