Lord Coe says public trust in athletics may not return until "way beyond" his four-year term as IAAF president.
Last Thursday, a World Anti-Doping Agency independent report said "corruption was embedded" within the governing body.
Its author, Dick Pound, said some athletes from Russia and Turkey who failed drugs tests then paid bribes.
"If there are athletes out there and they think they have been subject to extortion, come and speak to me," Coe told BBC
"We need to understand how far and how wide this thing goes. If it's the tip of the iceberg, then come forward and make those claims."