The July 31 closure was announced in April by the clinic, which said it can't afford to continue performing abortions without provincial funding.
The New Brunswick government has refused to pay for abortions in private clinics and waged a 20-year battle with the now-late Dr. Henry Morgentaler over the Fredericton clinic.
New Brunswick is the only province with a private abortion clinic not receiving funding for the procedure.
The current fee for the procedure at the Morgentaler Clinic is $700 before 14 weeks of pregnancy, and $850 between 14 and 16 weeks.
The clinic performs about 60 per cent of abortions in New Brunswick, its officials say. About 600 abortions a year are performed at the Fredericton clinic.
Regulation 84-20 of the New Brunswick Medical Services Payment Act stipulates abortions are paid for only if they are performed in one of two approved hospitals, after being deemed medically necessary by two physicians.
Clinic supporters continue to call for the provincial government to repeal the regulation.
"The status quo is not acceptable," said Judy Burwell of Reproductive Justice NB.
"Reproductive Justice NB, The Fredericton Youth Feminists and supporters from across Canada will not stop until safe and timely abortion services, covered by medicare, are available whether performed in a hospital setting or a medical clinic."
Halifax LEAF, a branch of the National Women's Legal Education and Action Fund, also demanded Friday for the regulation to be repealed.
Reproductive Justice NB began a crowdsourcing campaign earlier this month, hoping to secure the lease on the clinic building beyond July 31.
By Friday morning, it had surpassed its $100,000 goal with $111.776 raised through its campaign on FundRazr.