State Department spokesman Adam Ereli said there were "major irregularities and fraud" that are of "serious concern."
"Those instances of fraud and reports of major irregularity need to be investigated. They need to be investigated pursuant to Azerbaijani laws and regulations and in ways that redress grievances of people participating peacefully in the political system," Ereli said. "That is an important responsibility of any country that is committed to democracy and the rule of law and the rights of its citizens."
Ereli also said the United States is urging that all demonstrations in connection with the vote should be peaceful.
Speaking on state television yesterday, Azerbaijani President Ilham Aliyev acknowledged some irregularities in the elections, but is playing down criticism from the country's opposition and international observers.
Aliyev said his government will take serious steps to address shortcomings.
Results of the election show his ruling Yeni Azerbaycan Party remains by far the majority party.