"The voice of the Venezuelan people was not heard", State Department spokeswoman Heather Nauert said in a statement.
He also called on the opposition candidates, including those who were declared winners, to verify the entire process and called on the people to join together in new forms of protest.
While many Venezuelans express anger at the government, many too say they are frustrated with opposition leaders they perceive as disorganized.
The Democratic Union Roundtable coalition has refused to recognise the result and demanded a complete audit, campaign director Gerardo Blyde said.
Though the opposition expected to win the Sunday vote, the government swept 17 out of 23 state governorships.
The Trump administration has already imposed sanctions on Venezuelan officials, including Maduro.
The opposition accused the council of trying to suppress turnout among its base - a significant portion of which has grown disillusioned about the possibility of change and lost faith in leaders they perceive as disorganized and divided.
Hundreds have been lined up at some voting centers in Miranda, a state surrounding the nation's capital. Smartmatic, the U.K. -based company that provided the technology for the vote, said the results had been manipulated by at least 1 million ballots.
"The system is totally fraudulent", said Ocariz.
"I ask that we celebrate with joy, music, dance, but in peace, with respect to the adversary". "The regional elections were originally scheduled to take place last December, but the electoral council postponed the vote after polls indicated socialist candidates were widely slated to lose". The results, he said, were "suspicious". Some of the opposition did not participate in the elections stating they would be not be transparent. Some people were still in line waiting to cast ballots after the official closing time.
The opposition's electoral setback could further speed a flow of emigrants to other Latin American countries, Spain, and the United States, as many Venezuelans now fear the long-running political crisis will drag on for years.
"I was born in a democracy and I want to die in a democracy", she said.
Socialist candidates, invoking the popular Chavez at every rally, urged Venezuelans to vote against the opposition "candidates of violence", whom they accuse of plotting a coup under the veneer of peaceful protest. It's not clear whether the US would so quickly move to controversial sector sanctions before month end amortization payments.
After the election, the opposition will seek to throw the focus back to its main demands: guarantees of free and fair conditions for the 2018 presidential vote, freedom for jailed activists, foreign humanitarian aid and authority for congress.