BOGOTA, July 25 (Reuters) - Colombian President Alvaro Uribe warned right-wing paramilitaries on Wednesday that they will lose their benefits under a peace deal if they follow through on threats to stop cooperating with investigators.

The standoff threatens to unravel the accord under which 31,000 "paras" have demobilized over the last three years.

Former militia fighters say they will not give testimony or turn over illegally acquired wealth after a recent Supreme Court decision barring them from running for public office.

Some refused to answer questions from prosecutors in televised hearings on Wednesday, citing the court ruling they say denies them their right to participate in politics.

"If they don't obey the law they are going to lose their benefits," the conservative Uribe said. "Nobody wins by suspending testimony or suspending the turning over of assets."

Paramilitaries guilty of massacre, torture and cocaine trafficking face no more than eight years in prison under the peace accord. But to qualify for the deal, they have to confess their crimes and turn over wealth acquired through years of extortion and drug smuggling.

The paramilitaries were organized in the 1980s to protect cattle ranchers, drug lords and other rich Colombians from Marxist rebels. By the late 1990s both the rebels and the paramilitaries had directly entered Colombia's multibillion-dollar cocaine trade.

Thousands are killed in the conflict every year.

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