Mr Maduro and Mr Biden met briefly after President Dilma Rousseff's inauguration ceremony in Brasilia.
"I have demanded this time what we had demanded from the US 1,000 times before: a relationship based on respect, nothing else," said Mr Maduro.
Last month the US imposed sanctions on high-level Venezuelan officials.
The bill targets current and former Venezuelan officials who directed "significant acts of violence or serious human rights abuses against persons associated with the anti-government protests in Venezuela that began on 4 February".
Mr Maduro said he met Mr Biden after coming out of a bilateral meeting with Ms Rousseff at the Planalto presidential palace.
He described the meeting as "cordial and respectful".
"We have a government in Venezuela that complies with international law and is appreciated and supported by the whole continent," Mr Maduro told journalists.
"I believe he realised during his time here [in Brazil] that we have a relationship of cordiality and fraternity within our diversity."
"There is room for everyone in Latin America, and the Americans must understand that," said Mr Maduro.
More than 40 people from both sides of the political divide were killed in protests which took place in Venezuela between February and May.
The government said opposition leaders had incited protesters to violence and had been planning a coup against President Maduro.
The opposition said its activists had been unfairly targeted for their political convictions.
US sanctions were approved by both houses of the American Congress and are expected to be signed into law by President Obama.
The bill has caused further friction between the two countries.
They have had difficult relations since the election of the socialist President Hugo Chavez in 1998. Mr Chavez died in 2013 and was succeeded by Mr Maduro.
Venezuela and the US last had ambassadors in each other's capitals in 2010.
But any chances of a rapprochement may be boosted by the recent agreement between the US and Cuba - Venezuela's main ally - to restore diplomatic relations after more than 50 years of hostilities.
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