UN Secretary General Ban Ki-moon said Afghan voters had shown "courage and determination".
Turnout has been put at 40%. However, there were many reports of fraud that may question the results.
More than 2,500 candidates are vying for 249 seats in the lower house of parliament, or Wolesi Jirga.
Governor targeted Most polling stations had opened on schedule on Saturday.
However, the Taliban staged a series of rocket and other attacks around the country to deter voters.
The interior ministry said three security officials and 11 civilians had been killed.
The Kandahar provincial governor was also targeted in a bomb attack but survived.Faizal Ahmad Manawi, head of the Independent Election Commission (IEC), said initial figures pointed to a turnout figure of 40%. Turnout for the last parliamentary election, in 2005, was about 50%.
"As a whole I would rate this election successful," he said.
Gen Petraeus said the "people of Afghanistan sent a powerful message".
"The voice of Afghanistan's future does not belong to the violent extremists and terror networks. It belongs to the people," he said.
Gen Petraeus also praised the Afghan forces for "safeguarding a weapon with greater potential than any other - the people's right to vote".
Nato senior civilian representative in Afghanistan, Mark Sedwill, said the poll had shown "the future of Afghanistan remains one where violence cannot overthrow the democratic will of the people".
However the UN envoy to the country, Staffan de Mistura, told the BBC that it was premature to say the vote had been a success.
He said there had clearly been security problems, particularly in the south, but that in many other parts of the country the vote had been "enthusiastic".