"Much of the combat took place in the Ecuadorian territory, (and) it appears that the FARC entered the Ecuadorian territory," said Correa.
"The incident must be clarified a bit," he said.
Correa later on Saturday recalled his ambassador to Colombia for consultation.
Correa's call was echoed by his Venezuelan counterpart, who also called on the Colombian government to "clarify this."
Chavez's remarks were regarded as his most belligerent comments to date in a diplomatic dispute with Bogota, which was sparked by the hostage issue.
Chavez had been trying to mediate between the FARC and the Colombian government for the release of hundreds of hostages.
However, Uribe in last November abruptly called a halt to Chavez's mediation role, saying Chavez had spoken directly with a Colombian general about the hostage issue, which was a violation of their agreement.
Chavez responded by putting the ties "in the freezer" and withdrew the Venezuelan ambassador from Bogota, saying Colombia deserved a better president.
Uribe, meanwhile, accused Chavez of "coming to Colombia to interfere (in Colombia's domestic affairs) and promote an expansionist project" on the continent.
Chavez, despite his oral war with Uribe, this year has helped to facilitate the unilateral release of six high-profile hostages who had been held by the FARC for several years.
Humanitarian concerns mounted
Reyes' death came just three days after the FARC unilaterally released four former Colombian legislators it had held hostage for six years, the second such move this year. On January 10, the group released two Colombians – Clara Rojas and Consuelo Gonzalez.
The FARC is seeking a swap of some 40 high-value captives, including Ingrid Betancourt, a French-Colombian citizen kidnapped by the FARC in 2002 while campaigning for the presidency, with the Colombian government for 500 imprisoned FARC members, including some extradited to the United States.
