A type of breast implant linked to a rare cancer can still be sold in the United States, even though it has been banned in many other countries, the Food and Drug Administration said on Thursday.

The implants, which have a textured or slightly roughened surface, as opposed to a smooth covering, have been associated with a cancer of the immune system called anaplastic large-cell lymphoma.

The vast majority of the cases have occurred in women with textured implants, mainly those made by Allergan. But the F.D.A. said that the risk, though increased, was still low, and that there was not enough data to justify banning the implants.

It also said that in some patients with lymphoma, the type of implant was not known, so smooth implants could not be ruled out as a cause.