We would like the accord with the United States to be projected throughout the continent," Uribe told a business conference in the city of Medellin.
"We would like to have it with Brazil," he said. "I do not see this pact with the United States as incompatible with having pacts with other countries as well."
Under the deal, the US military will be able to operate on Colombian soil to tackle drug-trafficking and terrorism. Colombia's foreign ministry said that Bogotá had agreed the text of the deal with Washington: "this agreement reaffirms the commitment of both parties in the fight against drug-trafficking and terrorism".
The deal will now be reviewed in both countries before being signed.
A number of South American countries, mainly Venezuela, Ecuador and Bolivia, have condemned the plan as a threat to regional stability, others have supported Colombia's "sovereign" decision (Peru, Chile, Paraguay); Argentina stated the bases are "not helpful" and Brazil called for a meeting between President Obama and regional leaders.
Brazilian President Luiz Inácio Lula da Silva said that "the climate of unease disturbs me" and he also supported that the controversy be debated in depth by the Union of South American Nations, Unasur, which is scheduled to hold an extraordinary summit at the end of August in Bariloche, Argentine Patagonia.
Brazil, South America's biggest country and largest economy, is building up its armed forces as part of a push to increase its role on the world stage.
Washington has given billions of dollars in military assistance to Colombia, helping Uribe put the insurgents on the defensive. But the country remains the world's biggest producer of cocaine.
The US has been forced to look for a new base to counter drug trafficking and terrorism operations after Ecuador refused to renew the lease on its Manta base, which the US military was using.
Venezuelan President Hugo Chavez said the Colombian move would amount to preparation for an invasion of his country by US forces. Mr Chavez warned that "the winds of war were beginning to blow" across the region.
Last week President Uribe visited several of his South American neighbors to try to calm fears over the proposed deal with Washington.
Mercopress