A new campaign to get more women elected as Tory MPs is demanding "radical" changes in the way the party chooses its candidates.
Mrs May is among Women2Win's supporters
The Women2Win campaign wants positive action, such as creating an A-list of candidates - half of them women - for top Conservative target seats.
The group does not back all-women candidate short lists, but it wants to raise money to back women candidates.
The Tories have 17 woman MPs - 9% of the parliamentary party.
That compares with Labour's 28% and the Lib Dems' 15%.
The Conservatives had 118 women candidates at the last general election, but there have been complaints that too few of them are being chosen for winnable seats.
The campaign says the Conservatives had 13 women MPs in 1932 and 73 years later had added only four more.
Labour: 98 (28%)
Conservative: 17 (8.6%)
Lib Dems: 9 (15%)
All MPs: 127 (20%)
Source: Hansard Society
At the current rate of progress, it would take another 400 years for there to be an equal mix of male and female Tory MPs.
The group wants people to sign a declaration calling for "any positive and radical reforms of the selection procedures" short of all-women shortlists.
At the campaign launch, shadow cabinet minister Theresa May challenged leadership contenders David Cameron and David Davis to back the call for reform.
Mrs May, a Cameron supporter, said: "It is a little-known fact that there are more men in the shadow cabinet called David than there are women."
Mrs May has proposed an A-list of 50 men and 50 women to stand in the top 100 Tory seats.
But there are concerns that the idea would leave the last constituencies to choose their candidates with little choice.
An alternative being proposed to counter that problem is to have a 120-strong list, still divided equally between the sexes, for the top 100 seats.
The move would mean at least 40 female Tories would contest the top target seats.
The group says that whichever method is chosen it should only be used until 2015, by when campaigners hope to achieve their aims.
It also aims to raise money to support women candidates and encourage more women to become involved in politics and stand for election.
And it will provide training and professional advice to women candidates, as well as mentoring and support.
Six shadow cabinet ministers are backing the campaign: Mrs May, Caroline Spelman, David Willetts, Oliver Letwin, Michael Ancram and Andrew Lansley.
One of the Tory MPs supporting the campaign, Peter Viggers, said: "If we simply speak with the voice of 35-plus people with pretty wives, two children and a spaniel, we will not look as if we understand what the country needs."
But other MPs resist any moves towards positive discrimination.
Former minister Ann Widdecombe says women MPs must be able to look their male colleagues in the eye by undergoing the same process to become elected.
Among the leadership rivals, Mr Cameron says he would look at the idea of an A-list.
Mr Davis rejects the idea, saying local Tory associations should keep their autonomy. But he says he would launch a drive to recruit more female candidates.