Planned Parenthood Federation of America said it will immediately stop accepting reimbursements for supplying fetal tissue for medical research, an attempt to tamp down a controversy that has led to Republican investigations in Congress and an effort to end federal funding.

Planned Parenthood President Cecile Richards said in a letter Tuesday to the National Institutes of Health that the organization’s affiliates will no longer accept any reimbursement for costs associated with procuring tissue from abortions and providing...