"At this challenging time of President Hugo Chavez's passing, the United States reaffirms its support for the Venezuelan people and its interest in developing a constructive relationship with the Venezuelan government," Obama said in a statement.
"As Venezuela begins a new chapter in its history, the United States remains committed to policies that promote democratic principles, the rule of law, and respect for human rights," he said.
Chavez died on Tuesday after a two-year battle with cancer, ending the socialist leader's 14-year rule of the South American country.
"It's a moment of deep pain," Vice President Nicolas Maduro said in a televised speech on Tuesday, accompanied by senior ministers, his voice choking.
Chavez easily won a new six-year term at an election in October and his death will devastate millions of supporters who adored his charismatic style, anti-U.S. rhetoric and oil-financed policies that brought subsidized food and free health clinics to long-neglected slums.
Detractors, however, saw his one-man style, gleeful nationalizations and often harsh treatment of opponents as traits of an egotistical dictator whose misplaced statist economics wasted a historic bonanza of oil revenues.
Chavez's death opens the way for a new election that will test whether his socialist "revolution" can live on without his dominant personality at the helm.
Maduro favorite to win election
The vote should be held within 30 days and will likely pit Maduro against Henrique Capriles, the centrist opposition leader and state governor who lost to Chavez in the October election.
One recent opinion poll gave Maduro a strong lead.
Maduro is Chavez's preferred successor, enjoys support among many of the working class and could benefit from an inevitable surge of emotion in the coming days.
But the president's death could also trigger in-fighting in a leftist coalition that ranges from hard-left intellectuals to army officers and businessmen.
Venezuela has the world's largest oil reserves and some of the most heavily traded bonds, so investors will be highly sensitive to any signs of political instability.
A defeat for Maduro would bring major changes to Venezuela and could also upend its alliances with Latin American countries that have relied on Chavez's oil-funded largesse - most notably with communist-led Cuba, which recovered from financial ruin in the 1990s thanks largely to Chavez's aid.
Chavez was a garrulous figurehead for a global "anti-imperialist" alliance stretching as far as Belarus and Iran, and he will be sorely missed by anti-U.S. agitators.