The US has urged Colombia and Ecuador to seek a diplomatic solution to the crisis sparked when Bogota sent troops over the border to target Farc rebels.
Ecuadorean troops have been flying to the border area
Senior rebel leader Raul Reyes and 16 other militants died in the raid.
As tension grew, Ecuador and Venezuela moved troops to their borders, and Quito reportedly cut diplomatic ties.
A top Bogota official meanwhile accused both Ecuador and Venezuela of having ties with the Farc, and said the rebels had tried to buy uranium.
National police chief Oscar Naranjo said his information had come from documents found during the raid on the rebel camp in Ecuador.
"When they mention negotiations for 50 kilos of uranium, this means that the Farc are taking big steps in the world of terrorism to become a global aggressor. We're not talking of domestic guerrilla but transnational terrorism," said Gen Naranjo.
Other documents showed that Venezuela's President Chavez had provided $300m (£151m) to the Farc, and had received funds from them many years earlier, he said.
And there was also evidence of links between the Farc and representatives of the Ecuadorean government, Gen Naranjo said.
"This unmasks the relations of the Farc with a series of governments, with a series of personalities, some public, some more sinister," Gen Naranjo said.
In the Venezuelan capital, Caracas, senior figures poured scorn on the claims that Mr Chavez had financed the rebels.
"We are accustomed to the lies of the Colombian government," said Vice-President Ramon Carrizalez. "Whatever they say has no importance.
"They can invent anything now to try to get out of that violation of Ecuadorean territory that they committed."
Ecuadorean President Rafael Correa angrily denied the suggestion that his administration had links with the rebels.
"They said we had a pact with terrorists, and that is completely false," he said during a cabinet meeting.
"We are dealing with an extremely cynical government."
Both Ecuador and Venezuela withdrew their ambassadors from Bogota in the wake of the incursion. Ecuador announced on Monday that it was severing all diplomatic ties, the Colombian foreign ministry said.
Ecuador was flying troops by helicopter towards the border area on Monday, while President Chavez said he was deploying tanks and troops to Venezuela's own border with Colombia.
Voices urge restraint
As the crisis threatened to deepen, UN Secretary General Ban Ki-moon added his voice to those calling for restraint.
"The secretary general is concerned about the increased tensions and heightened rhetoric emerging over the weekend involving Colombia and its neighbours, Ecuador and Venezuela," a UN statement said.
Brazil and other regional powers have also urged calm. Spain and a number of Latin American countries have offered to mediate in the dispute.
In Washington, a state department spokesman backed Colombia's right to defend itself and urged dialogue.
"From our perspective this is an issue between Colombia and Ecuador," Tom Casey added.
"I'm not sure what this has to do with Venezuela."
Colombia's government has received billions of dollars in aid from Washington to fight the Farc.
Colombia's foreign minister said he regretted that troops had to cross the border, but said it had been necessary "in the fight against terrorism".
"The Colombian government has never wanted to disrespect or violate the sovereignty or integrity of the sister republic of Ecuador," Fernando Araujo said.
HAVE YOUR SAY
Colombia and President Uribe have been fighting a civil war for 40 years, and it's pretty bad. Mr Uribe is trying very hard but these fallouts with other nations are dangerously ignorant and harmful to the region.
Alex Dominguez, Milwaukee
French Foreign Minister Bernard Kouchner meanwhile said the death of Reyes was "bad news", as he had been France's contact in its efforts to free French-Colombian Farc hostage Ingrid Betancourt.
"It is bad news that the man we were talking to, with whom we had contacts, has been killed," Mr Kouchner said on France Inter radio.
Ms Betancourt, a former Colombian presidential candidate, has been held for six years and is said to be in very poor health.
Six hostages have been released since Mr Chavez began efforts to win their freedom.
Colombia initially invited him to mediate, but later tried to exclude him from the process.