A draft opinion suggests the US Supreme Court could be poised to overturn the landmark 1973 Roe v Wade case that legalised abortion nationwide.
In the recently leaked documents, Justice Samuel Alito wrote the Roe v Wade decision was "egregiously wrong".
If the top US court strikes down the ruling, "trigger laws" could instantly make abortion illegal in 22 US states. The justices are not expected to issue a ruling until early July.
The reports have caused outrage on both sides of the Atlantic, with politicians in Scotland ramping up calls for the Scottish Government to install buffer zones to prevent protesters from being able to pressure people using abortion services.
Responding to the US development, Ms Sturgeon said: “The right of women to decide what happens to our own bodies is a human right.
"And experience tells us that removing the legal right to abortion doesn’t stop abortions happening – it just makes them unsafe and puts the lives of women at much greater risk #RoeVWade.”
However, Labour MSP Monica Lennon accused Ms Sturgeon of “not lifting a finger to protect women”.
Mr Cole-Hamilton said: “We must make sure that we protect the rights of women to access safe and legal abortion in the UK without harassment.
“For years, campaigners, including myself, have been calling for buffer zones around abortion clinics to ensure that people in a time of need are not faced with intimidation and shame at a time when they deserve support and empathy.
“No one thinks that Nicola Sturgeon and Maree Todd have anything in common with the US Republican party and its legal assault on personal freedoms, but the fact is that they have stalled and dissembled over these buffer zones for far too long.”
Scottish Labour leader Anas Sarwar said the leaked documents were “horrifying”, adding that overturning the ruling would be a “massive, massive step backwards” for the rights of women.
He said he was “not for a second suggesting that the Scottish Government would associate themselves in any way” with the events in the US, but stressed “dither and delay” on the introduction of buffer zones “is not acceptable”.
Pro-choice campaigners and MSPs continue to mount pressure on the Scottish Government over implementing anti-abortion protest buffer zones across Scotland.
Last month more than 100 anti-abortion activists gathered outside the Queen Elizabeth University Hospital in Glasgow.
Campaign group Back Off Scotland says implementing 150m buffer zones, backed in the SNP’s manifesto and the Programme for Government, was “crucial” to protecting women’s access to healthcare.
Ms Sturgeon said last week there were “some complex legal issues involved” in implementing zones.
She said any laws which were passed needed to “be compliant” with other areas such as the European Convention of Human Rights Act.
Ms Lennon said: “I agree with Nicola Sturgeon that women should have the right to decide what happens to their own bodies. That right, however, is under attack in Scotland and she hasn’t lifted a finger to protect women.
"The anti-abortion lobby is getting bolder each day that the SNP Government fails to legislate on protest-free buffer zones at abortion clinics.
"If the First Minister really wants to show solidarity with women around the world, she should lead by example and instruct her Government to introduce emergency legislation to protect abortion rights in Scotland. No more excuses.”
Pro-choice group Back Off Scotland said the First Minister’s words only “goes so far”.
Addressing Ms Sturgeon’s comments via Twitter, Back Off Scotland tweeted: “You’re the First Minister, you have a Women’s health minister and the Lord Advocate in your Cabinet.
"You MUST uphold reproductive rights in this country and introduce buffer zones NOW.”
A draft member’s bill on buffer zones brought forward by Green MSP Gillian Mackay is expected to be published by mid this month. However, this could take more than a year to implement.
Scottish Labour leader Anas Sarwar backed calls from Ms Lennon for the Scottish Government to enact national legislation around buffer zones as he said any delay was “unnecessary”.
Back Off Scotland said they were “speechless” at suggestions abortion laws in America could potentially be repealed.
Women’s health minister Maree Todd previously claimed councils can enact by-laws to ban certain protests.
However Cosla, the governing body for local councils, sought legal advice, which said it would need to come from the Scottish Government.