Nicola Sturgeon heard from women left suffering from mesh, including those who are now dying following complications.
Campaigners presented demands, including for proposed mesh removal treatment and training by expert American clinician Dr Dionysios Veronikis, to be completed by spring 2020.
The same deadline was given for an independent review into the mesh complications service to report and for a complex mesh case review unit to be operational.
Campaigners want a halt on non-urgent mesh removal procedures until these steps are in place.
They also want a ban on the purchase of pelvic mesh implants in Scotland.
Dr Veronikis withdrew his offer to come to Scotland to perform surgery last month, alleging "delays and disrespectful behaviours" by the medical authorities.
Now, at a meeting in Glasgow, Ms Sturgeon said an "agreement in principle" has been reached for him to visit next year.
Scottish Mesh Survivors campaigner Olive McIlroy said: "I'm confident that he will get here but the trust has been lost and to get that repaired is going to take a long long time.
"We need help now. We've always campaigned to help others and never ourselves, this is the first time we've actually asked for something to help us."
She said she and other mesh survivors would want to meet Dr Veronikis for a consultation on possible mesh removal.
Ms McIlroy thanked the First Minister for her time, adding: "This has been going on for eight years and this has been the first time we've actually got to speak to the First Minister.
"She gave us plenty of time ... she did listen, it depends how she is going to react."
Scottish Conservative leader Jackson Carlaw, who has championed the women's cause alongside Labour MSP Neil Findlay and former SNP health secretary Alex Neil, also thanked Ms
Sturgeon for meeting the campaigners and hearing "harrowing" testimony.
He said: "We heard from women who are dying now of complications arising from mesh.
"Having done so much to ensure that women in the future don't suffer from mesh implants, today was about women who hope something can be done to remove mesh from them and give them their lives back."
Ms Sturgeon said she updated the women on the work the Scottish Government is doing to ensure women access treatment they need.
She said: "I am absolutely committed to and determined that we will do everything possible to get these women the treatment and the care that they need but also that we take steps to answer any questions that they have about their past treatment and the circumstances of that.
"A wide range of issues have been raised today and I've given them a commitment that systematically one by one we will work through them."
She said following a meeting with Dr Veronikis in the US there is an agreement in principle for him to come to Scotland next year, pending requirements such as securing a temporary licence to practice in the UK.