The escalation of tensions was triggered over the weekend when Colombia troops crossed the border with Ecuador and killed Raul Reyes, a top commander of the Colombian FARC rebels who had set up a camp there.
Chavez, who sympathizes with the leftist rebels, condemned the killing and angrily ordered about 9,000 soldiers - 10 battalions - to Venezuela's border with Colombia. He warned Colombian President Alvaro Uribe that any strike on Venezuelan soil could provoke a South American war.
Uribe said he has provided Chavez with precise information on the location of rebel camps in Venezuela. He said one was home to Ivan Marquez, another top leader of the Revolutionary Armed Forces of Colombia, or FARC.
But Uribe said he would not allow his nation to be drawn into a conflict with its neighbors.
"Colombia has never been a country to go to war with its neighbors," Uribe said. "We are not mobilizing troops, nor advancing toward war with neighbors."
President Bush said the United States will stand by Colombia and criticized Venezuela's government for making "provocative maneuvers." Colombia has received some $5 billion in U.S. aid to fight drugs and leftist rebels since 2000.
Retired Venezuelan Gen. Alberto Muller Rojas, a former top Chavez aide, told The Associated Press the troops were being sent to the border region as "a preventative measure."
Soldiers boarded buses and trucks at the Paramaracay base in central Venezuela on Tuesday morning, and battalions also were moving out from the northern state of Lara, pro-Chavez Gov. Luis Reyes said.
The Venezuelan military has been tightlipped about troop movements. Venezuela's armed forces include about 100,000 troops, Muller Rojas said. Colombia's U.S.-equipped and trained military has more than twice as many.
Uribe said his government would ask the International Criminal Court to try Chavez for "genocide" for allegedly financing the FARC, the country's main rebel group. He cited a reference to a $300 million Venezuelan payment in documents found in a laptop the Colombians said belonged to Reyes.
Colombia said documents in Reyes' laptop also indicate that Ecuador' internal security minister met recently with a FARC envoy to discuss deepening relations with Ecuador, and even replacing military officers who might oppose that.
Both Venezuela and Ecuador expelled Colombia's ambassadors in the wake of the attack and dismissed the allegations as lies.
The biggest losers from the killing of Reyes appeared to be the hostages that FARC rebels have held for years, pending a swap with rebel prisoners. Along with Reyes, 20 other rebels were killed in the raid.
Ecuador and France said they had been communicating with Reyes, trying to secure a hostage release.
"I'm sorry to tell you that the conversations were pretty advanced to free 12 hostages," Ecuador's leftist president, Rafael Correa, said in a nationally televised address. "All of this was frustrated by the war-mongering, authoritarian hands" of the Colombian government.
French Foreign Ministry spokeswoman Pascale Andreani confirmed that France was in contact with Reyes as well, and that "the Colombians were aware of it."
Publicly, there had been no indication of even preliminary progress in securing the release of any of the 40 hostages the FARC wants to swap for hundreds of jailed guerrillas.
Those hostages include three U.S. military contractors and former Colombian presidential candidate Ingrid Betancourt, a dual French national who has become a cause celebre in Europe.
The rebels said in a communique that Reyes died "completing a mission to arrange, through President Chavez, a meeting with (French) President (Nicolas) Sarkozy" aimed at securing Betancourt's release.
Saturday's raid came on the heels of the FARC's release last week of four hostages to Venezuelan Justice Minister Ramon Rodriguez Chacin. The minister said the raid proved the "intent of the fascist Colombian government is to hamper the handover of hostages, because that is the path of peace."
Several Latin American leftist leaders have suggested the U.S. was intimately involved in executing the raid that killed Reyes. Colombian military officials have said U.S. satellite intelligence and communications intercepts have been key to putting the FARC on the defensive.
On Tuesday, a spokesman for the U.S. Southern Command would neither confirm or deny American military participation. "We do provide intelligence support to partner nations but I can't get into details on operations," Jose Ruiz told the AP from Miami.
Another victim of the crisis may be border trade worth $5 billion a year, most of it Colombian exports sorely needed by Venezuelans already suffering milk and meat shortages.
Venezuela said it would stop new exports and imports. At one closed border crossing, in Paraguachon, Venezuela, authorities stopped trucks lined up for about a half a mile Tuesday morning. But traffic was flowing normally at another crossing, in El Amparo, where a handful of Venezuelan troops stood watch as usual, the customs office was open and traffic passed freely.
In Ecuador, where Correa sent 3,200 troops Monday to reinforce the border, there was no halt to trade worth about $1.8 billion annually, said Carlos Lopez, the undersecretary of immigration.
Correa, on a regional tour to rally other Latin American leaders against Colombia, said in Peru that his military has "captured" 47 rebel camps in Ecuador since he took office last year.
"And they ask me if we are accomplices of the FARC?"