Colombian President Alvaro Uribe on Wednesday agreed to rebel demands that a leftist senator mediate the release of hostages but only if all 24 police and soldiers held by the guerrillas are freed at the same time.

Previous talks had broken down with the rebels insisting that Senator Piedad Cordoba help mediate liberations and Uribe saying no. The president had accused Cordoba of trying to use hostage releases for her own political gain.

The fiery senator from northern Colombia has negotiated the release of other hostages held by the Revolutionary Armed Forces of Colombia, or FARC, making her a national political figure rumored as a possible presidential candidate.

"All 24 hostages must be freed simultaneously," Uribe told a news conference. He also called on the rebels to hand over the bodies of three hostages who have died in captivity.

Uribe said the International Committee of the Red Cross and the Catholic Church can also be involved in the hostage talks.

Earlier this year Cordoba was in negotiations aimed at freeing Pablo Moncayo, a soldier taken by the FARC in 1997. But with political rivalries heightened ahead of next year's presidential vote, the government broke off the talks.

The soldier's father, Gustavo Moncayo, has led a campaign for the release of kidnap victims, draping himself in chains and walking throughout Colombia.

By authorizing Cordoba as a mediator, the president was seen making a rare concession to the guerrillas. The FARC, which killed Uribe's father in a 1983 kidnapping attempt, issued no immediate response to the announcement.

Some opposition politicians and family members of hostages who were considered first in line to be released under previous talks said Uribe's condition that all 24 be freed at once would delay any deal.

"He is impeding Pablo's release," Gustavo Moncayo said.

The guerrillas are in a 45-year-old war to impose socialism in this Andean country. Since the 1980s the conflict has been fueled by Colombia's cocaine trade, with a mosaic of illegal armed groups fighting over lucrative smuggling routes.

Since Uribe was first elected in 2002, his hard-line security policies have pushed the rebels out of major cities and off highways where they once kidnapped with impunity.

The president is flirting with the idea of running for an unprecedented third term in 2010 if his supporters succeed in changing the constitution to allow him to campaign. (Editing by Jackie Frank)