Conservative MP Fiona Bruce spoke out as members of the trade union prepare to vote on the proposal during the BMA's annual conference in Bournemouth.
She told the Mail on Sunday: "Instead of listening to lobby groups, the BMA should be listening to British women, 70 per cent of whom want the abortion time limit to be lowered from the current 24 weeks limit - one of the highest in the Western world."
The motion proposes that the BMA supports the removal of legal sanctions on abortions conducted "up to viability" - generally interpreted to mean up to 24 weeks.
Opponents fear passing the motion could prompt pro-choice campaigners to step up their efforts to push through reforms, such as increasing the abortion limit - currently set at 24 weeks.
Catholic members of the BMA have been urged by the Catholic Bishops Conference of Scotland to side against the motion during a vote on Tuesday.
In a letter, Director of the Catholic Parliamentary Office Anthony Horan said: "To build a more just world we need to ensure that every individual is afforded the right to life, this means a world free of abortion."
The BMA was quoted by the Mail on Sunday as saying "all viewpoints" on abortion will be debated at its annual conference.
The organisation also said it recognised abortion was "a sensitive and complex issue and one on which doctors have a range of views."