Calls for Labour to bar men from standing in by-elections have received a frosty response from party leader Jeremy Corbyn.
Jess Phillips, who heads the women's parliamentary Labour Party, insisted the radical move would be a key factor in achieving gender parity among MPs.
However, Mr Corbyn gave the idea a cool reception.
The Labour leader told the Press Association: "That wouldn't necessarily achieve parity because you don't know when the by-elections are going to fall, or who is going to be successful in those by-elections.
"What I want to do is achieve at least 50% of the parliamentary Labour Party being women. We will do that, the national executive is meeting next month and will be considering a whole lot of processes, because a lot of new selections are going to take place, and I will do my very best to make sure we achieve that.
"I should also say that my shadow cabinet has well over 50% of women."
With the Tories determined to cut the number of constituencies from 650 to 600, observers believe the re-drawing of boundaries could badly impact on the current number of women Labour MPs.
Ms Phillips, MP for Birmingham Yardley, said: "I think the Labour Party has to make every seat an all women shortlist until we get equality.
"Currently 44% of Labour seats are held by women. We want 50% equality in this party, and for Jeremy to commit to this on the public record.
"Women are more likely to have a marginal seat so when your boundary shifts, you're more likely to lose your seat."
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