Gulf residents and politicians from the region have criticized Mr. Feinberg as taking too long to cut checks to restaurant and resort owners, shrimpers and others whose livelihoods have suffered since the April spill.
He has said many of the claims came with improper documentation and so couldn't be processed.
As of Thursday, Mr. Feinberg had paid 163,946 claims for a total outlay of $2.4 billion. Claimants were able to seek emergency payments up until Nov. 23. They have until August 2013 to make claims for a final, lump-sum payment, but to do so means they must give up their right to sue BP or any of the companies tied to the spill.
Mr. Feinberg said 10,000 claimants have applied for final payments.
Starting this week, claimants who have received an emergency payment can opt to receive a final payment—$25,000 for businesses or $5,000 for individuals. Mr. Feinberg said the process would avoid the tangle of paperwork needed to file other claims, requiring no more than checking a box on a form and signing a release not to sue.
Payments would be made within two weeks, he said.
"That allows the facility to clear out those eligible claimants who already received compensation and feel that compensation they received is adequate," Mr. Feinberg said.
Those claimants, he said can "take this quick pay option and be done with it."
The fund was set up as an attempt by BP to head off pending litigation against the company. Its offshore spill, which ranked as the worst in U.S. history, led to widespread economic and environmental damage, including the closing of Gulf waters to fishing. The new plan is designed to further that mission.
"The twin goals of this program have always been to corral all of the claims so that we can try and bring finality to the process and make people who are innocent victims of the spill whole," Mr. Feinberg said in an interview.
Another option for people who say they have been harmed: They can opt to receive quarterly payments until they decide whether to make a final claim. The quarterly payments could mean these claimants receive a smaller final payment if the financial climate in the Gulf improves in coming months, Mr. Feinberg said.
"We'll cut you obviously a much smaller check but the advantage of that approach is you can wait and see and not surrender your rights to sue," he said.
Mr. Feinberg also will announce Monday that anyone who wants a lawyer to help them sort through the new options can have one for free. At the request of Mississippi Attorney General Jim Hood, Mr. Feinberg plans to hire a firm to offer the free legal services to claimants.
He also pledged to hire more local residents to staff claims offices after criticisms that he had bypassed locals for those jobs in areas still smarting from the spill.