Cristina Fernandez, Argentina's president, is also expected in the Venezuelan capital on Thursday for a meeting with Chavez.
The Colombian military operation which triggered the crisis killed Raul Reyes, a commander of the Revolutionary Armed Forces of Colombia (Farc), in Ecuador.
Ecuador and Venezuela have since cut diplomatic ties with Colombia, and on Wednesday Correa called Alvaro Uribe, the country's president, "a psychotic liar".
The Caracas meeting is part of a move to drum up international support against Colombia.
Ecuador claims Colombia violated its sovereignty by carrying out the strike on its territory.
Attempting to ease the diplomatic crisis, the Organisation of American States (OAS) approved a resolution on Wednesday that called the Colombian operation a violation of Ecuadorean sovereignty.
Correa, however, said the resolution was not enough.
"The OAS resolution pleases us. We are pleased, but not satisfied," he said after his meeting with Chavez.
"This isn't going to cool down until the aggressor is condemned."
Wednesday's resolution called for Jose Miguel Insulza, the OAS secretary-general, to lead a delegation to both Ecuador and Colombia to ease tensions, but stopped short of explicitly condemning the assault.
The US was the only OAS member to offer Bogota unqualified support.
Colombia has accused both Chavez and Correa of aiding the Farc, labelled by Washington as a "terrorist" organisation, and said this was shown by documents found on a laptop seized at the bombed rebel camp.
It said that documents found on Reyes after the attack indicated that Venezuela gave Farc $300 million.
On Thursday, Francisco Santos, Colombia's vice-president, said he saw no risk of war with Venezuela or Ecuador despite the military mobilisation.
Correa has demanded a clear condemnation
of Colombia's action by the OAS [EPA]
"I don't think there is a risk of war. The Colombian government has been very clear it won't use force," Santos said on Thursday during a visit to Brussels for talks with EU officials.
"It won't fall into the game of provocation."
Santos said Colombia was justified in launching the raid because it had repeatedly asked Ecuador, as well as Venezuela, in vain to take action against Farc camps on their territory.
Santos said his government was prepared to take further measures to solve the situation on condition that the Farc is not allowed to set up camps close to Colombia's borders.