"We do have to be concerned about terrorism. We have to be concerned about the safety and well-being of countries in the region," she said.
A recent Colombian raid on a Farc (Revolutionary Armed Forces of Colombia) rebel base in Ecuador sparked a week-long diplomatic crisis which saw Venezuela and Ecuador send troops to their Colombian borders.
Colombia said it found computer records in the rebel camp showing Chavez paid the Farc $300 million.
Bogota defused the crisis that erupted over its cross-border raid by apologising and promising not to take similar action if its neighbours co-operated in fighting the Farc.
|Farc rebels have waged a 40-year war against |
the Colombian government [GALLO\GETTY]
On Wednesday Bush accused Chavez of using his country's oil wealth to create anti-US sentiment in Latin America.
The stand-off with Colombia, he said, was "the latest step in a disturbing pattern of provocative behavior by the regime in Caracas".
Eliana Cardoso, a Brazilian political economist, told Al Jazeera the underlying reasons behind the conflict remained.
"Uribe is trying very hard to get rid of the guerillas but by now the guerillas are not only a domestic issue but have penetrated the borders of the neighbouring countries," he said.
"The protection that Venezuela is giving to the guerillas is something that we have to be worried about."
Rice's talks with Lula and Celso Amorim, the Brazilian foreign minister, also covered trade, climate change, the UN Security Council, the Middle East and biofuel production, the Brazilian foreign ministry said.
The US secretary of state also signed a joint action plan that would see Brazil and the US sharing information to battle racial discrimination.
However Cardoso said Rice's visit was unlikely to be a sign that Bush administration was beginning to take more interest in Latin America.
"I don't think it really represents a very concrete interest in the region because this interest has turned during the last decade to the Middle East.
"They are concerned about conflicts in Middle East, they are concerned about oil in the Middle East."
Rice will also visit the Brazilian city of Salvador, the heart of the African-Brazilian community, before heading on to Chile to meet Michelle Bachelet, the president.