More than 100 activists from the 40 Days of Life group gathered on a road approaching the Queen Elizabeth University Hospital on Sunday.
In a letter to Women’s Health Minister Maree Todd, 76 consultants from the hospital accused the group of intimidation and harassment.
The BBC has contacted the 40 Days for Life group for comment.
The group, which was founded in Texas in 2004, has previously said its members were staging public prayers for a “culture of life” over the Christian period of Lent, and it was not their intention to upset people.
The letter, written by the campaign group Back Off and signed by doctors working at the Queen Elizabeth University Hospital, says thousands of woman having an abortion in Scotland have been subject to protests over the years.
The doctors are backing calls for clinics to have protest-free buffer zones similar to those being introduced in Northern Ireland.
The letter reads: “As well as being our patients, these women are our sisters, daughters and colleagues. They deserve compassion and support.
“They should be spared the deplorable intimidation and harassment which they currently receive from protesters. This group seeks to restrict women’s access to healthcare.”
The letter called on the Scottish government to pass a Safe Access Zone Bill, banning activities intended to deter or prevent women from accessing abortion care within 150 metres of a clinic entrance.
Similar measures have been introduced in Spain, Australia and most recently in Northern Ireland.
Ealing Council in London was the first authority in the UK to use anti-social behaviour laws to create “buffer zones” outside abortion clinics – using legislation available in England.
Women ‘vulnerable and upset’
Lead signatory and consultant paediatric radiologist Dr Greg Irwin said he was seriously concerned about the protests taking place outside the Glasgow hospital, and their impact on the delivery of care.
He said: “We know first-hand how distressing this harassment is for our patients, which makes it infuriating for us as clinical staff to have to pass these groups day-in-day-out.
“These women may well be feeling vulnerable and upset. They should not have to put up with judgement or intimidation outside our hospital.
“How can we offer our patients the standard of care and support they deserve in this situation? Implementing buffer zones is essential to deal with this problem, both in Glasgow and throughout Scotland.”
Woman’s Health Minister Maree Todd said she looked forward to Green MSP Gillian Mackay bringing forward a members’ bill on buffer zones.
She said she had also convened a working group to consider the issue of protests outside abortion clinics.
She added: “The Scottish government is committed to women being able to access timely abortion without judgement. I condemn, in the strongest possible terms, any attempts to intimidate women as they choose to access abortion services.”