It comes as Nicola Sturgeon is set to begin a visit to the US on Monday.
Campaign group Abortion Rights Scotland addressed the gathering of around 100 people on Regent Terrace, and the event was supported by Back Off Scotland.
Local councillors and representatives from several trade unions also attended.
Green MSP Gillian Mackay told the crowd it is “in no way acceptable” for anti-abortion campaigners to gather outside hospitals in Scotland.
Ms Mackay hopes to introduce a members bill next week about the introduction of buffer zones.
Labour MSP Monica Lennon called on the First Minister to take “action not words” on the subject of abortion rights during her upcoming visit to the US.
The protest was organised by Lindsay Jaacks, 34, an American living in Edinburgh.
She said: “When the news was leaked about Roe vs Wade I just felt so helpless, and I wanted to organise this as a place for people, not just Americans, who were really concerned about what this meant for abortion rights here in Scotland.”