US Secretary of State John Kerry said the massive turnout, which could see opposition leader Aung San Suu Kyis party catapulted to power, was a "testament to the courage and sacrifice shown by the people of Burma over many decades."
"While these elections were an important step forward, we recognize that they were far from perfect," Kerry added.
"There remain important structural and systemic impediments to the realization of full democratic and civilian government," AFP quoted.
The top US diplomat pointed to a large number of unelected seats reserved for the military, the disfranchisement of minorities such as Rohingya Muslims and the "arbitrary" disqualification of certain candidates.
Millions of people cast their ballots for the first time in a quarter of a century, in an event heavy with history and filled with emotion.
Early indications were of an 80 percent turnout.
"We will continue to watch the vote counting process, and encourage all parties to help ensure the tabulation is transparent and credible and any complaints are addressed promptly, transparently and appropriately," Kerry said.
"Todays election has the potential to be an important step towards greater peace, prosperity and democracy for the people of Burma," he added, encouraging political leaders to work together.
"The United States remains committed to supporting the people of Burma in their pursuit of democracy, development, and national reconciliation going forward."