The commitment comes as Gillian Mackay MSP has proposed a Bill that would introduce national legislation for safe access zones around healthcare settings that provide abortion services.
The British Pregnancy Advisory Service separately urged Westminster to follow Holyrood’s lead and bring in legislation to create “buffer zones” around abortion centres.
Speaking at Holyrood, Ms Sturgeon said theGovernment would take a “range of actions to improve women’s access to healthcare”.
A women’s health ambassador will also be announced.
Ms Sturgeon said: "We will work with Gillian Mackay, and MSPs across the chamber, to safeguard the access of women to abortion services without harassment or intimidation.”
Campaign group Back Off Scotland has welcomed the commitment from the First Minister as the body said it would ensure national legislation around buffer zones will pass when it goes through Parliament.
Lucy Grieve, co-founder of Back Off Scotland, said: “We are delighted by the First Minister’s announcement today.
"The Scottish Government’s commitment to back Gillian Mackay MSP’s Safe Access Zones Bill means that this legislation will pass when it comes before the Scottish Parliament. With the full legal might and resources of Government behind us, it is now time to turn our focus to making as robust a Bill as possible.
"This is a hugely significant step in the journey towards harassment-free access to abortion services in Scotland, and Back Off Scotland looks forward to working closely with Gillian Mackay and the Scottish Government going forward.”
Ms Mackay also welcomed the commitment to support her members’ Bill to introduce buffer zones outside clinics.
The Green MSP said: “This is a landmark moment and we will make progress quickly to ensure those accessing healthcare can do so without intimidation.”
In the coming year, the Government will also consult on specific draft laws to give effect to the recommendations in Helena Kennedy’s report on tackling misogynistic behaviours.
The Government intends to introduce a Misogyny and Criminal Justice Bill and a Bill to improve the way complaints about the police are managed.
The First Minister has said a Criminal Justice Bill will be introduced that will provide for the abolition of the not-proven verdict.
Ms Sturgeon held a ‘mini’ abortion care summit on Monday last week involving local council representatives and women’s health minister Maree Todd that discussed the potential use of bylaws to implement 150-m buffer zones around abortion care providers at a local level in Scotland.
The meeting followed a summit on abortion care in June, which saw the Government commit to considering to trial the zones via the local authority regulations.
The Supreme Court is considering whether the Abortion Services (Safe Access Zones) (Northern Ireland) Bill is outside the legislative competence of the Northern Ireland Assembly.
The Government is waiting on the outcome of this ruling – expected in autumn – before they implement their own safe access zone measures.