Members of Iraqi security forces cast ballots early ahead of the overall Saturday vote, the first since parliamentary elections in 2010. More than 15 million Iraqis are eligible to vote. At least 8,000 candidates are competing for 378 provincial council seats.
Kobler said that all eyes are focused on the Saturday election now that Iraqi police and military personnel have voted.
"It is of the utmost importance that voters turn out in an orderly and safe environment free of violence, threats and intimidation," he said in a statement.
His comment preceded a series of attacks Monday. Those attacks left at least 25 people dead and more than 170 others injured. Most of the attacks targeted Shiite areas of Baghdad, security sources told CNN.
Al-Qaida in Iraq, a Sunni group, claimed responsibility for many of the attacks in recent months.
Kobler, in a weekend statement, condemned the assassination of Najm al-Harbi, leader of the Iraqiya political coalition in Diyala province. Iraqiya challenged Iraqi Prime Minister Nouri al-Maliki, a Shiite, in 2010 elections.