Nearly two-thirds of all people in Scotland who responded to a consultation on the issue said they are against the change and many religious groups, including the Catholic Church and the Church of Scotland, are bitterly opposed to it.
Ms Sturgeon insisted churches, and individuals within them, would not have to conduct same-sex marriages if they do not agree with them.
The decision to change the law to allow gay couples to marry, rather than enter a civil partnership (as they can do currently), comes after almost 80,000 people responded to the Scottish government consultation.
The Scottish government now intends to have a “focused consultation” with a number of interested parties before drafting the legislation. This will allow ministers to consider what other possible protection can be included, “to give reassurance to those who have expressed concerns”, Ms Sturgeon added.
Draft legislation should then be published by the end of the year, on which further consultation would be held.
The Scottish government is also holding talks with the Home Office as ministers at Holyrood believe an amendment is needed to UK equalities legislation to protect individual celebrants who do not want to conduct same-sex ceremonies, even if their church, as an organisation, backs them.
The Scottish government is working “very constructively” with Westminster on this, Ms Sturgeon said.
If the legislation is introduced in 2013, as planned, the first same-sex marriages could take place at the start of 2015.
The UK Government has also carried out a consultation on same-sex marriage in England and Wales, and has said it will publish the result of that by the end of the year.