The leaders of the main political parties in Scotland have outlined their party’s commitments to advancing LGBT rights regarding each potential outcome of the independence referendum.

The leaders of the SNP, Scottish Labour Party, Scottish Conservatives, Scottish Liberal Democrats, Scottish Green Party, and the Scottish Socialist Party, made the commitments in response to a letter from the Equality Network.

The organisation, which is neutral on the referendum, sought commitments in six areas of law and policy, including the constitution, equality law, public services, foreign affairs, and the asylum system.

In the event that Scotland votes for independence on 18 September, five of the six parties say they will support protections for LGBT equality in a written constitution, including on the grounds of sexual orientation, gender identity, and intersex status.

The Scottish Conservatives did not make a commitment, with leader Ruth Davidson stating it was “up to the people of Scotland to decide what provisions are included”.

In the event that Scotland votes to remain in the UK, the SNP, Scottish Green Party, and Scottish Socialist Party are committed to seeking the devolution of equality law, currently reserved to Westminster.

The Liberal Democrats said that power over equality law could potentially be shared between both parliaments as part of a federal UK; the Scottish Labour Party committed to devolving the enforcement of equality law, but not the powers to change the law itself, and the Scottish Conservatives made no commitment but said specifically that equal pension provisions were “best dealt with at a UK level”.

Equality law is already fully devolved in Northern Ireland.

Tom French, policy coordinator for the Equality Network, said: “The outcome of the independence referendum has the potential to make a significant impact on LGBTI equality in Scotland, whether through changes to legal protections, powers, resources, policies, or the shape of our public services.

“When voters are being asked to make a choice between two futures for Scotland we think it’s important that we have as much information as possible about the intentions and commitments of the parties that will shape these futures.

“Regardless of the outcome of the referendum the Equality Network will continue to work with parties on all sides of the debate to secure the best deal for LGBTI equality and human rights.”

SNP First Minister Alex Salmond said: “Independence is a once in a lifetime opportunity to embed and enhance LGBTI rights… With a No vote we face the prospect of another Tory government committed to scrapping the Human Rights Act…It’s only with the full powers of an independent country that we can finally secure true equality for LGBTI people and a fairer society for all.”

Scottish Labour leader Johann Lamont said: “Whilst we are in no way complacent, we do not believe that anything further could or would be achieved under a different constitutional settlement. But the record of devolution in Scotland, and the Labour Party as the architect of devolution, speaks volumes for what we can achieve in the future.”