The Society for the Protection of Unborn Children (SPUC) argued the decision by ministers to allow women to take the drug misoprostol to induce abortion at home was “unlawful” and a threat to women’s health.
However, Judge Lady Wise rejected the group’s arguments in a ruling earlier this year, following a two-day hearing at the Court of Session in May.
SPUC appealed against the decision.
An appeal hearing is being held at the court on Tuesday.
The society’s chief executive John Deighan said: “We were disappointed by the original decision, but it was always our intention to fight this case all the way.
“Our position and beliefs remain the same.
“After thorough consideration of the judgement and in tandem with legal advice we now appeal the decision.
“We owe it to our supporters who continue to make donations to cover our legal costs.”
Campaigners launched the judicial review legal action after Scotland’s Chief Medical Officer, Dr Catherine Calderwood, last year confirmed she had written to all Scottish health boards to indicate misoprostol could be taken by women outside a clinical setting.