BRASILIA, Brazil — Secretary of State Rice yesterday urged nations such as Venezuela to meet their U.N. obligations and keep terrorists out of their territories. “Borders are important. But borders cannot be a means by which terrorists hide and engage in activities that kill innocent civilians,” Ms. Rice said after meeting with Brazilian leaders on a two-day trip to South America.

Her comments come a day after President Bush said Venezuela’s response to the recent crisis in Colombia and Ecuador was “the latest step in a disturbing pattern of provocative behavior by the regime in Caracas.”

The Bush administration is ramping up its tough talk against the Venezuelan president, Hugo Chavez, while at the same time praising its South American allies for holding strong against terrorism.

The latest rhetoric, including discussion of whether Venezuela should be designated a state sponsor of terror, is aimed at isolating Mr. Chavez and building stronger alliances inside Latin America at a time when American foreign policy remains deeply unpopular throughout the world.

Ms. Rice planned to visit Chile after her stop in Brazil, using the opportunity to engage leaders who the administration says have been helpful to American economic and anti-terrorism efforts. Left out of Ms. Rice’s itinerary are those countries that have been critical of America, including Argentina.

Ms. Rice met yesterday morning with the Brazilian president, Luis Inácio Lula da Silva, and foreign minister, Celso Amorim.

While the leaders discussed such issues as the economy and the use of biofuels, overshadowing their agenda was the recent clash in Ecuador.

Earlier this month, Mr. Chavez and Ecuador’s president, Rafael Correa, ordered troops to their Colombian borders and withdrew their ambassadors from Bogota after Colombia killed a top rebel leader, Raul Reyes, on Ecuadorean soil.

During the raid, Colombia obtained computer hard drives that American officials say show the Venezuelan government may have had dealings with the Revolutionary Armed Forces of Colombia, which America regards as a terrorist group.

When asked whether America was considering designating Venezuela a state sponsor of terror, Ms. Rice said: “We will watch the situation and act accordingly.”

On Wednesday, Mr. Bush said, “The region is facing an increasingly stark choice: to quietly accept the vision of the terrorists and the demagogues, or to actively support democratic leaders like President Uribe” of Colombia.

“I’ve made my choice. I’m standing with courageous leadership that believes in freedom and peace,” Mr. Bush said.