WASHINGTON—The administrator of the $20 billion fund established to compensate victims of the Gulf oil spill said he didn't know if the amount would be enough to help all those who would ultimately be affected.

Kenneth Feinberg, named last month by the White House to oversee the process of awarding claims, said he wouldn't know the full scope of legitimate requests as long as oil continued to gush from the broken well a mile beneath the ocean's surface.

"Until the oil stops, you don't know how pervasive the oil spill will be, so you don't know if somebody who has not been harmed at all today will be harmed by additional oil next week," he told CNN's "State of the Union" on Sunday.

"Once the oil stops, I believe we'll be able to very quickly get a handle on the comprehensiveness of the claims population."

BP agreed last month to pay out $20 billion to an independently managed fund over four years under pressure from the Obama administration. The agreement doesn't cap the company's liabilities in the spill, however.