More than 1000 troops backed by helicopter gunships are hunting down several hundred rebels believed to be heading for the nearby border with Ecuador to seek refuge from the fighting, army officials said.
"The murder of our soldiers pains us greatly," Uribe said on Sunday after holding crisis talks with military commanders in Puerto Asis, 530km southwest of Bogota.
"But to make concessions to terrorism or to bow to terrorism undermines democracy," he said.
Uribe added that he intends to discuss the situation along the border with Ecuadorean authorities.
"To make concessions to terrorism or to bow to terrorism undermines democracy"
President of Colombia
As many as 300 members of the Revolutionary Armed Forces of Colombia, or FARC, on Saturday attacked oil wells near Puerto Asis and ambushed an army convoy, killing at least 19 soldiers.
Rebel casualty figures were not known.
Another 19 soldiers who went missing during the combat were found alive and well early Sunday, acting Army chief General Hernan Alonso Ortiz. The soldiers got separated from their unit during the clashes and had been unable to contact their commanders.
Six soldiers were also killed on Saturday when they fought rebels blockading a road in northeast Colombia - making it the deadliest day for the military since Uribe came to power three years ago on pledges of crushing the 40-year-old insurgency.
Before going into a meeting with Uribe in Puerto Asis, Mayor Jorge Eliecer Coral said he was going to ask the president to boost security along the border with Ecuador.
Cross border rebels
"We are fed up that insurgents cross over from Ecuador to commit crimes in our lands," Coral said.
For years, FARC guerrillas have slipped across the 640km border into Ecuador's northern jungle region to seek refuge from battle and to buy supplies.
The FARC has this year launched some of its boldest attacks on the military since peace talks collapsed in February 2002, killing more than 130 soldiers.
The rebel offensive came after military commanders claimed that a US-backed, three-year-old military build-up ordered by Uribe had forced the FARC into irreversible decline.
Analysts say the FARC wants to undermine Uribe's re-election hopes by showing that his security crackdown has failed and that only peace talks with a leader more sympathetic to the rebels can lead to peace.
"These attacks are a sign that the FARC is gearing up for a military escalation ahead of the May 2006 elections to show that (Uribe's) democratic security policy is a failure," said professor Roman Ortiz, a terrorism expert at Los Andes University.
Uribe's security policy against
FARC is failing, say experts
The Constitutional Court, the country's highest judicial authority, has yet to rule on whether Uribe can seek a second consecutive term.
Army officials maintain the FARC is made up of 12,000 fighters now, down from 18,000 a year ago, due to deaths, captures and desertions brought on by the government offensive.
Colombia's drug-fueled conflict pits the FARC and the smaller National Liberation Army against a handful of right-wing paramilitary militias and government forces, killing more than 3000 people every year.