About half of the eligible voters took part in weekend provincial council elections, the first since U.S. combat forces left Iraq in December 2011.
Kobler praised Iraqi elections officials for their ability to plan the election in a tense security environment. He said Iraqi security forces deserve credit for ensuring the elections were largely peaceful.
"Credible elections are critical to the country's stability," he said in a statement.
About 50 people were killed in attacks throughout Iraq in the week leading up to the elections.
More than 8,000 candidates competed for 400 or so seats in provincial councils. Some candidates were assassinated before the election and violence in Iraq prompted authorities to suspend elections in Ninevah and Anbar provinces.
Kobler said the government needed to reschedule Anbar and Ninevah elections as soon as possible. Anbar was the seat of the Iraqi insurgency during the height of the war.