Mike Jackson, chief executive of Birmingham Midshires, said the RBS offer was no longer high enough, given a 50 per cent rise in the value of retail banks since last August, when the deal was struck.
"Given the advice which the society has received, the board cannot now recommend that our members vote in favour of a transfer at a price which we no longer believe to be fair and reasonable."
The society's U-turn means the prospect of a windfall worth pounds 630 each to the society's 1 million members has temporarily been withdrawn.
The Building Societies Commission said details of the RBS offer could not be put to members without the board's recommendation.
Both Birmingham Midshires and Halifax yesterday called for RBS to release Midshires from a legally binding agreement which blocks the society from discussing other bids. Halifax has offered pounds 780m, potentially boosting windfalls by at least pounds 150 each.
Gary Marsh, director of corporate affairs at Halifax, said: "It's a farcical situation that in a sense is becoming more farcical.
"They are not recommending the RBS offer, the RBS are saying they are considering their position, and the society can't send [an offer] to its members. RBS should recognise reality and withdraw."
Royal Bank of Scotland hit back by indicating it would consider legal action over the deal - action which could force Midshires to stick with the lower offer or block it from handing out windfalls.Reuse content