A cross-party group of MSPs are calling for the power to legislate for gender quotas to be devolved to the Scottish Parliament.
The politicians want control of quotas to be included in the new package of powers promised to Holyrood in the wake of the independence referendum.
They are calling for Scotland to introduce gender quotas for political parties, with "robust sanctions" for non-compliance, stating that voluntary party quotas to secure gender equality have proved insufficient.
Writing in the Scotland on Sunday newspaper, Labour MSP Kezia Dugdale and Green MSP Alison Johnstone say: "At the moment the power to bring in legal quotas in the Scottish Parliament is currently reserved to Westminster, under the provision on political parties in the Scotland Act 1998.
"As politicians discuss 'extensive new powers' for the Scottish Parliament, we would like to see the power to legislate for gender quotas devolved.
"We want every political party to support gender quotas in their manifestos for the 2016 Holyrood elections. And we want to see change by 2020."
They state that at present around 35% of Holyrood's MSPs are women, while less than a quarter of councillors are female.
Their demand is supported by SNP MSP Marco Biagi, Lib Dem MSP Alison McInnes, Labour MSP Jackie Baillie and independent MSP Jean Urquhart.
The call for gender equality in politics comes as Nicola Sturgeon bids to become Scotland's first female First Minister with her campaign to replace Alex Salmond as SNP leader.
Her appointment would mean that the three main parties in Scotland would all be led by women, with Johann Lamont for Labour and Ruth Davidson for the Tories.
Writing in the Mail on Sunday, Ms Sturgeon said: "I also hope that, by standing to be First Minister, I can send a message to every woman and girl in our land - that in 21st century Scotland, if you are good enough and work hard enough, there is no glass ceiling on ambition."
The cross-party group hopes the power over gender quotas will be included in the package to be devised by the new Smith Devolution Commission.
Lord Smith of Kelvin, who was appointed to lead the commission, has called on Scotland's five main political parties to take a ''principled-led approach'' to devolution, which draws from their existing published proposals for more powers but also takes account of the result of the referendum.
He has asked the parties to submit their proposals by October 10.
Meanwhile, unionist parties are being warned that they must deliver a set of powers which meets the expectations of the Scottish people, or face election defeat and a "cascade to independence".
Labour, the Tories and the Lib Dems had set out separate proposals for further devolution before the referendum, with the parties' Westminster leaders coming together before the crucial vote to jointly pledge "extensive new powers" under a swift timetable.
Writing in the Sunday Times, Dave Watson, head of bargaining and campaigns at trade union Unison Scotland, said: "Perhaps the biggest challenge is for Labour, whose fiscal plans were the weakest.
"If the 'change' mantra is to be credible, Labour needs to be more radical in its approach to the commission.
"Without such change the much-quoted 'slippery slope' will become a cascade to independence."
Mr Watson said fully devolving income tax is "the starting point", while he would also add National Insurance.
Elsewhere, independence supporter Sir Sean Connery said: "Cameron and the other Westminster leaders made big promises to Scotland to get the No vote, and they are going to have to deliver big.
"Otherwise the SNP will trounce them in the next election. The sensible solution is for Scotland to be in charge of all its tax and spending.
"That way, no-one could complain about who funds who."
Commenting on the call for quotas, Scottish Conservative MSP Murdo Fraser said: "The Scottish Conservatives, with two senior leaders in succession, have a very strong track record of promoting women into leading positions.
"Amongst our own female members there is a view that positive discrimination is not just unnecessary, but also insulting to those who have made it to the top under their own efforts."
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