Obama, in an interview with US Spanish-language network Univision, said the entire region "has been watching the violence, the protests, the crackdowns on the opposition" following the controversial April 14 election.
Maduro defeated opposition leader Henrique Capriles, at least officially, by a razor-thin margin in the election to replace the late leftist leader Hugo Chavez.
Capriles however has refused to concede defeat, claiming there were irregularities.
"I think our general view has been that it's up to the people of Venezuela to choose their leaders in legitimate elections," said Obama, who was in Costa Rica for a summit with Central American leaders.
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"It's based on the notion of our basic principles of human rights and democracy and freedom of press and freedom of assembly. Are those being observed? There are reports that they have not been fully observed post-election."
Tensions have been running high since the election to replace the larger-than-life Chavez.
The government says nine people died in protests in the days after the election.
Opposition and pro-government lawmakers exchanged punches and kicks in a spectacular brawl at the National Assembly on Tuesday.
Each side held dueling May Day marches on Wednesday, with Maduro calling Capriles a "crybaby" who could not accept defeat.