(Recasts and updates with new details from president, adds byline)

By Patrick Markey

BOGOTA, April 2 (Reuters) - Colombian President Alvaro Uribe said on Wednesday he would extradite the first former paramilitary warlord to face U.S. justice after he violated a government peace deal by ordering crimes from his prison cell.

Colombia's Supreme Court earlier authorized Carlos "Macaco" Jimenez to be sent for trial on drug-running and other charges in a U.S. court for crimes committed during the darker days of the Andean country's four-decade-old conflict.

Under their peace deal, U.S. extradition warrants for the paramilitary bosses were suspended, provided they surrendered, gave up crime, confessed to massacres and murders and vowed to compensate victims in exchange for short prison terms.

"The government has announced this decision and intends to fulfill it," Uribe said when asked by reporters about the court ruling. "It is simple: those who comply with their obligations ... will not be at risk."

He said the extradition order was already being processed through the interior ministry and the president's judicial office.

The ruling came as U.S. Democrats are demanding Washington ally Uribe do more to control paramilitary influence and better protect labor union workers from militia threats before they approve a U.S. free trade deal for his Andean country.

Violence has eased under Uribe as his U.S.-backed military takes back regions once under the control of rebels or illegal paramilitaries. The main rebel group, the Revolutionary Armed Forces of Colombia or FARC, has been forced into remote areas.

Set up by rich landlords in the 1980s, the paramilitaries were initially a response to rebels in areas with weak state presence. But they flourished into drug gangs who took over land and massacred peasants, sometimes in league with state forces.

Jimenez, who once led the Central Bolivar Bloc, one of the most powerful paramilitary gangs, was expelled from the peace agreement in August when authorities charged he had violated the terms of the deal.

Under Uribe's government, more than 30,000 paramilitary fighters demobilized and the president credits the program in part for a drop in violence and kidnapping from the conflict.

But human rights groups say Uribe has been too lenient with paramilitary commanders. Critics say militia bosses have kept their criminal empires intact and failed to live up to their end of the accord to confess and compensate victims.

Uribe is also facing a scandal linking some of his lawmaker allies to the paramilitary death squads. Dozens of lawmakers and politicians have been jailed and are under investigation for ties to the militia commanders.

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