Bush refrained from mentioning his leftist nemesis when asked during a press conference after meeting with Uruguayan President Tabare Vazquez whether Chavez should be considered a threat.
"I've come to South America and Central America to advance a positive, constructive diplomacy that is being conducted by my government on behalf of the American people," Bush said.
"I would call our diplomacy quiet and effective diplomacy."
Deeply unpopular in Latin America because of the Iraq war and U.S. trade and immigration policies, Bush is pushing a softer message aimed at improving his reputation and bolstering U.S. influence in the region.
Chavez blames U.S.-backed free-market policies for increasing poverty in Latin America and has embarked on a counter-tour during Bush's visit.
Bush traveled by helicopter on Saturday to meet Vazquez at his presidential retreat in Anchorena Park, some 125 miles (200 km) west of Montevideo.