WASHINGTON (AP) — The Obama administration on Thursday announced a $1.25 billion deal with black farmers that could end a years-long stalemate over alleged racial discrimination by the Agriculture Department.

If approved by Congress, it would be the second round of damages stemming from a class-action lawsuit the government originally settled in 1999. The new money is intended for people who were denied earlier payments because they missed deadlines for filing. The amount of money each would get depends on how many claims are successfully filed.

President Obama initially called for the $1.25 billion in his budget last year, but the request stalled in Congress as disagreements persisted over the amount of funding and the structure of the settlement. Agriculture Secretary Tom Vilsack said Thursday’s agreement should pave the way for congressional approval and get money flowing soon.

In a statement, Obama said the deal would bring ‘‘these long-ignored claims of African-American farmers to a rightful conclusion.’’

‘‘I look forward to a swift resolution to this issue, so that the families affected can move on with their lives,’’ Obama said.

Vilsack said the deal should close a ‘‘sordid chapter’’ in USDA history in which blacks often lost land or went deeply into debt after being denied loans and other aid that routinely went to their white counterparts.

John Boyd, a key plaintiff organizer and head of the National Black Farmers Association, initially balked at the $1.25 billion last year, saying it would take more money to satisfy all the claims. But he said Thursday that he and others agreed to the total because the case has dragged on for so long.

‘‘Many of the farmers have already died waiting for justice so I thought this was the right thing to do,’’ he said.

The original lawsuit is known as Pigford, named after Timothy Pigford, a black farmer from North Carolina who was among the original plaintiffs. Under the 1999 settlement, the government paid out more than $1 billion to about 16,000 farmers, mostly from the South.

Most claimants opted for expedited $50,000 payments that required a relatively low burden of proof. Boyd and others have pushed for another round of damages because thousands of people said they didn’t know about the settlement and missed deadlines for filing.

The new agreement calls for a similar process in which claimants can win damages without going to court.

Associate Attorney General Thomas Perrelli said claimants can seek fast-track payments of up to $50,000 plus debt relief, or choose a longer process for damages of up to $250,000. Estimates on the number of potential claims vary widely, but some expect about 65,000 — which would set average payments at roughly $20,000.

Thursday’s announcement comes as Boyd and others had become increasingly critical of Obama, arguing that he was paying lip service to the issue and not living up to a campaign promise to fund it. It also represents a shift from the Bush administration, which resisted paying new claims.

Roy Merrick, who tried unsuccessfully in the early 1980s to start a catfish farm on his property in Natchez, Miss., said Thursday he was glad to hear he might get some compensation. He said he could never get USDA officials to pay him much attention when he tried to get a loan — even thought many of his white neighbors got federal help to build successful catfish ponds.

‘‘Had I been able to secure money back in those times I might have been able to do more for my family,’’ said Merrick, 67, who instead went into home painting and repairs.