Previous talks had broken down with the Revolutionary Armed Forces of Colombia, or FARC, insisting that Senator Piedad Cordoba help mediate and Uribe saying no. The Colombian leader had accused Cordoba, a leftist, of trying to use hostage releases for her political gain.
By authorizing her mediation, 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.
The fiery senator from northern Colombia has negotiated the release of other FARC kidnap victims, enhancing her profile and spurring rumors she may run for the presidency in 2010.
"All 24 hostages must be freed simultaneously," Uribe, a pro-business conservative who is flirting with running for a third term next year, told a news conference. He also called on rebels to hand over the bodies of three hostages who have died in captivity.
Cordoba called the announcement "a positive gesture" and said she will ask to meet with Uribe soon to set the stage for talks. The president said the Red Cross and the Catholic Church can also be involved in any upcoming hostage negotiations.
Earlier this year Cordoba was in talks aimed at freeing Pablo Moncayo, a soldier seized by the FARC in 1997. But with political rivalries heightened ahead of next year's presidential vote, Uribe broke off the mediation.
The soldier's father, Gustavo Moncayo, has led a campaign for the release of kidnap victims, draping himself in chains and walking throughout Colombia.
Some opposition politicians and relatives of hostages who were considered first in line to be released under previous talks said Uribe's condition that all 24 police and soldiers be freed at the same time 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 Colombia. Since the 1980s the conflict has been fueled by the nation'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.
His supporters are trying to change the constitution to allow him to campaign for an unprecedented third term.
