The majority of those taking part in a Scottish Government consultation on the issue said they thought people should be given the legal right to identify as “non-binary”.
Two thirds also agreed that the age at which people can apply to legally change their gender should be lowered from 18 to 16, with the process made simpler and easier.
The consultation, which attracted more than 15,000 responses, was launched more than a year ago as part of plans to make changes to the Gender Recognition Act 2004.
At the time, the then Equalities Secretary Angela Constance said the law in Scotland needed to be reformed so it treated transgender and non-binary people with “dignity, fairness and respect”.
The independent analysis of the consultation responses said 65 per cent of Scottish respondents wanted ministers to “take action to recognise non-binary people”.
Given a series of options, 56 per cent said they backed the “full recognition” of non-binary people by allowing them to take part in a new self-declaration system.
Under the current Act, people in the UK have to be over 18 and apply to a panel if they want to change their gender, but ministers want to make the “intrusive and onerous” process simpler.
They have suggested removing the need for applicants to provide medical evidence and to have lived in their new gender for two years, as well as setting the minimum age at 16.
The analysis showed that 66 per cent of Scottish respondents agreed with this proposal, with many noting that by the age of 16 people are already allowed to make other life-changing decisions.
A Scottish Government spokeswoman said: “We will consider this analysis and the views of consultees as we take forward our commitment to bring forward legislation on gender recognition.”
The consultation results were welcomed by the Scottish Trans Alliance, which said the public’s view on the issue was now “clear” given the high number of people taking part.
“While advancing equality for minority groups does not depend on opinion polling, it is always great to see high levels of consultation support,” said the group’s manager James Morton.
“We also welcome that opponents of the reforms have been able to freely share their views with the Government, as we believe that constructive dialogue and close scrutiny of legislation proposals is always helpful in ensuring there will be no unintended consequences.”
Simon Calvert of the Christian Institute, which is campaigning against changes to the Act, said the official recognition of a third gender could lead to confusion in the legal system.
“How many people really want to see 16-year-old children locking themselves into gender change at an age when many are still coming to terms with who they are?” he added.
“All the political posturing in the world can’t erase the hard-wired reality of male and female.”