Opposition parties calling for the introduction of “buffer zones” around clinics.
Aileen Campbell, speaking in her former brief as public health minister, said ministers were looking to see if action could be taken.
The claims have been branded an attempt to “suppress the truth” by pro-life campaigners, who claim they themselves have been subject to intimidation at the hands of “militant” pro-abortion groups.
It comes after NHS Lothian and Edinburgh City councillors expressed concern about patients and staff being intimidated outside facilities.
Ms Campbell revealed the Government is looking at the prospect of action in Holyrood answers to Liberal Democrat MSP Alex Cole Hamilton.
But the Edinburgh Western MSP called for ministers to go further and give Scottish councils the same powers they have south of the border to introduce “safe zones” to protect women from harassment.
“Designating buffer zones around abortion clinics is a smart way of ensuring women are able to access the medical treatment they need without fear of harassment,” Mr Cole-Hamilton said.
“The Scottish Government ought to look seriously at these proposals. It is possible to uphold freedom of speech and the right to protest peacefully while also ensuring women are able to attend medical appointments without intimidation. We should use the law to ensure that happens.”
Edinburgh Greens Councillor Claire Miller has called for the introduction of a buffer zone outside the Chalmers Centre on Lauriston Place after women attending medical appointments were allegedly subjected to “massively intimidating” situations by peaceful pro-life demonstrators.
At the recent Scottish Liberal Democrat Spring Conference, members voted in favour of both decriminalising abortion and introducing safe zones around clinics.
But Michael Robinson, director of campaigns for Society for the Protection of Unborn Children (SPUC) Scotland, hit out at the buffer zone call.
He said: “Proposals calling for buffer zones in Scotland display the ignorance of those making such calls. Firstly, there are no abortion clinics in Scotland. They take place in hospitals and it is typically impossible to identify women who may be attending for an abortion.
“Secondly, the claims of intimidation and harassment are completely without foundation; in fact it is the case that pro-life people have required the support of police to protect them from increasingly intolerant pro-abortion militants.
“Thirdly, the right to freedom of speech is a crucial foundation of any democratic society and has become a target simply because pro-abortion campaigners wish to suppress the truth of abortion even to the point of denying women the support which offers them a real alternative.”