Uribe flew to Medellin and spoke to relatives of the hostages
President Alvaro Uribe of Colombia has accepted responsibility for the death of 10 hostages - including two senior politicians - in a failed attempt to rescue them from rebels.
However he vowed to continue his fight against terrorism.
The guerrillas said the hostages died in crossfire, but the army says they were executed by rebels in a jungle camp, north-west of Medellin, capital of Antioquia province.
Some families of the victims criticised the government, saying they had opposed any rescue attempt and urged the authorities to pursue a negotiated solution to the hostage crisis.
The BBC's Jeremy McDermott in Medellin says the government will now be under increased pressure to exact revenge.
Three hostages survives Monday's failed rescue operation.
Among those who died were Antioquia Governor Guillermo Gaviria and former Defence Minister Gilberto Echeverri - who were captured during a peace march in Medellin more than a year ago.
They were being held by FARC guerrillas at the jungle camp with 11 soldiers and were part of a larger group of 80 hostages that the rebels wanted to trade for imprisoned comrades.
There are conflicting reports of what led up to the bloodshed, but the government has confirmed it had launched a rescue attempt.
Guerrillas said the hostages were killed when they became caught up in a gun battle as soldiers reached the camp, but the government says its troops did not open fire.
The family of Ingrid Betancourt, a presidential candidate being held captive by the FARC since last year, has called on President Uribe to refrain from launching fresh rescue attempts.
"Despite the pain, the president should think with a cool head and make the problem [of an exchange] a priority because the ends don't justify the means," said Yolanda Pulecio, the mother of Ms Betancourt.
But any chance of a peaceful humanitarian exchange of prisoners has now died with the hostages, our correspondent says.
President Uribe, whose father was killed by rebels and who is himself a former Antioquia governor, said his hardline policies would not change.
Gaviria had called on officials not to make concessions
"In this moment of pain, Colombia cannot surrender," he said.
"Now, we have to fortify our decision to defeat terrorism."
Mr Uribe was emotional as he described a phone call to Mr Echeverri's family.
"For me, it is a very hard blow that Gilberto Echeverri died in this way while I was president. That call I made painfully."
Mr Uribe took office last year promising to crack down on the guerrilla groups that have waged an insurgency for nearly 40 years.
But armed rebel groups have continued their campaigns of violence.
The FARC is still holding hundreds of hostages, including former presidential candidate Ingrid Betancourt, senators, governors, mayors, police officers and members of the military.
Three Americans who were captured when their surveillance plane was shot down earlier this year are also being held by the rebels.