The voting "will further discredit the government," State Department spokesman John Kirby said, after polling went ahead despite opposition protests that President Pierre Nkurunzizas candidacy was unconstitutional.
The voting took place amid gunfire and grenade blasts, and at least two people were reported killed, AFP reported.
Opposition and civil society groups have denounced Nkurunzizas candidacy as a breach of the constitution and of a 2006 peace deal that ended a dozen years of civil war.
"The governments insistence on going forward with Presidential elections on Tuesday risks its legitimacy in the eyes of its citizens and of the international community," Kirby said.
"More serious is the risk of unraveling the fragile progress made through the implementation of the Arusha Agreement, which states clearly that no Burundi president shall serve more than two terms in office," he added.