Planned Parenthood - which is the largest abortion provider in the US - quickly rejected the offer.
The group insists that federal funding, which amounts to about $500 million a year, is not used for abortion services.
Nevertheless, the institution said that it would not accept an offer that required an end to performing abortions.
Planned Parenthood has claimed that federal grants are used to provide other health-care services - although critics have demonstrated that Planned Parenthood clinics provide few other services for women.