US Secretary of State Condoleezza Rice has urged a "diplomatic resolution" to a crisis that has set Colombia against neighbours Venezuela and Ecuador.
Venezuela and Ecuador say they have deployed thousands of troops
Tensions have risen since Colombia on Saturday conducted a military raid in Ecuador, killing a Colombian Farc rebel leader and at least 16 others.
The presidents of Ecuador and Venezuela have called for clear international condemnation of Colombia's actions.
The two countries moved troops to their borders in response to the raid.
"The situation shows that everyone needs to be vigilant about the use of border areas by terrorist organisations like the Farc," Ms Rice told a news conference in Brussels after a meeting of Nato foreign ministers.
"Colombia is a good friend and I do hope there will be a diplomatic outcome," she said.
An opportunity for talks could arise in the Dominican Republic where regional leaders are gathering for a meeting of the Rio Group.
Latin American presidents, including those from Colombia, Venezuela and Ecuador, are expected to meet on Friday.
Venezuela says 9,000 soldiers have been moved to the border with Colombia, while Ecuador says 3,200 of its forces have been deployed.
The two countries have also cut diplomatic ties with Bogota in response to the incursion, which resulted in the death of senior Farc commander Raul Reyes.
Colombian President Alvaro Uribe has insisted that Colombia will not be drawn into a war with its neighbours.
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.
In a bid to calm the crisis, the Organisation of American States (OAS) on Wednesday unanimously approved a resolution saying that Colombia had violated the "principles of international law" by crossing into Ecuador.
The 34 OAS member states agreed to set up a commission of inquiry led by OAS head Jose Miguel Insulza to investigate the incursion and scheduled a meeting of OAS foreign ministers for 17 March.
March against violence
Ecuadorean President Rafael Correa, speaking in Caracas at a joint news conference with Venezuela's President Hugo Chavez, welcomed the resolution but said it was not enough.
Ecuador would not rest, he said, until the international community issued an explicit condemnation of Colombia.
Mr Chavez branded the Colombian raid a "war crime", adding that Bogota, which receives billions of dollars in aid from Washington to fight drug-trafficking, was just a "lackey of United States imperialism".
He dismissed 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).
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.
A month ago millions of Colombians around the world turned out to march against the violence of the Farc - a march that was supported by the Colombian government.
A similar march was held on Thursday, but this time against Colombia's right-wing paramilitaries.