The leaders of Ecuador and Venezuela have called for clear international condemnation of Colombia for its raid against rebels inside Ecuador.
Venezuela and Ecuador say they have deployed thousands of troops
"This isn't going to cool down until the aggressor is condemned," said Ecuadorean President Rafael Correa.
In a bid to calm the crisis, the Organisation of American States (OAS) criticised Colombia but stopped short of outright condemnation.
Ecuador and Venezuela moved troops to their borders after Saturday's raid.
Both countries also cut diplomatic ties with Bogota in response to the incursion, which resulted in the killing of a senior rebel commander, Raul Reyes, and 16 others.
Colombia has apologised to Ecuador but said the raid was necessary.
It said that its forces found documents linking both Ecuador and Venezuela to guerrillas from the Revolutionary Armed Forces of Colombia (Farc) - an accusation both countries reject.
Speaking on Thursday in Brussels, Colombian Vice President Francisco Santos said he saw no risk of war despite the military mobilisation.
"The Colombian government has been very clear it won't use force," Mr Santos told Reuters news agency.
"It won't fall into the game of provocation."
Venezuela says it has sent some 9,000 soldiers to its border with Colombia, while Ecuador says 3,200 of its forces have been deployed to the frontier with its neighbour.
In response to developments, the OAS unanimously approved a resolution saying that Colombia had violated the "principles of international law" by crossing into Ecuador.
During the emergency talks in Washington, the 34 OAS member states agreed to set up a commission of inquiry led by OAS head Jose Miguel Insulza to investigate the incursion.
A further meeting of OAS foreign ministers has been set for 17 March.
Mr Correa, speaking in Caracas at a joint news conference with Venezuela's President Hugo Chavez, welcomed the resolution but said it was not enough.
Analysts do not expect any actual military conflict
Ecuador would not rest, he said, until the international community issued an explicit condemnation of Colombia.
Mr Chavez, for his part, branded the Colombian raid a "war crime", adding that Bogota was just a "lackey of United States imperialism".
"We demand condemnation of the Colombian government for this aberrant act," said Mr Chavez, indicating that he would limit trade and investment with Colombia.
He poured scorn on Colombian claims that a laptop found during its raid on the rebel camp in Ecuador held files indicating that Venezuela had given the Farc $300m (£150m).
In Washington, Assistant Secretary of State for Western Hemisphere Affairs Tom Shannon said: "We are disturbed by information... that appears to indicate some of Colombia's neighbours were either unable or unwilling to address a known Farc presence in their countries."
The US, which gives Colombia billions of dollars in aid to fight the illegal drugs trade, was the only OAS member to give Colombia unqualified support.
Amid the war of words, US Defence Secretary Robert Gates said: "My personal view is that there's relatively little likelihood of military conflict."
The Farc, which has been fighting the Colombian state for more than four decades, is viewed by the US and the EU as a terrorist group.
It is thought to fund itself mainly through drug-trafficking and holds hundreds of hostages for ransom and political ends.