Earlier, the Islamic State group, which two weeks ago captured the Mosul Dam spanning the Tigris River just north of the city of Mosul, denied the claim, insisting it was still in control of the facility.
The retaking of the dam would mark the first major victory for the Iraqi and Kurdish forces battling the Islamic militants since U.S. airstrikes began earlier this month. However, the conflicting accounts that emerged Monday underscored the challenge facing Kurdish and Iraqi forces trying to reassert themselves after weeks of setbacks.
The dam and its broader complex hold great strategic value as they supply electricity and water to a large part of the country.
Al-Moussawi said early Monday that the Iraqi and Kurdish forces "hoisted the Iraqi flag over" the dam. He added that the troops were backed by a joint aerial support but didn't specify whether there were any U.S. airstrikes in the area of the dam Monday.
At least 170 bombs have been dismantled around the dam but many more remain, al-Moussawi also said in a televised statement. He added that militants fled to areas near the south of the complex, hiding in homes and offices on the premises.
Local residents and others in the area could not immediately be contacted to confirm the security forces' recapture of the dam.
Iraq's Defense Ministry said security forces "liberated a large part of the Mosul Dam" with the help of U.S. airstrikes, adding that forces are working to fully free the entire complex. In a statement, U.S. Central Command said it carried out 15 airstrikes near the dam Monday with fighter jets, bombers and drones.
In an online statement, the Islamic State earlier denied losing control of the dam, dismissing the government claim as "mere propaganda war." The statement, which could not be independently verified, was posted on a website frequently used by the militants.
The U.S. launched airstrikes against the Islamic State group in Iraq more than a week ago in a bid to halt its advance across the north. The U.S. military said U.S. forces conducted nine strikes Saturday and another 16 on Sunday.
The U.S. and France have agreed to arm Kurdish fighters — with the U.S. providing light weapons and ammunition. French Foreign Minister Laurent Fabius refused to specify the type of arms France would deliver, saying only they would be "sophisticated." The British and German governments have also stated their willingness to supply the Kurds with weapons.
The dam's seizure by Islamic State militants on Aug. 7 was part of a string of victories by the Sunni radical group as it looks to expand its hold in northern Iraq, driving back Kurdish forces, sending minority communities fleeing and unleashing a wave of violence over a territory straddling the Syria-Iraq border.
The decision to launch airstrikes marked the first direct U.S. military intervention in Iraq since the last American troops withdrew in 2011 and reflected growing international concern about the extremist group.
The White House sent a letter to Congress on Sunday saying that its air campaign in Iraq "is consistent with the president's directive that the U.S. military protect U.S. personnel and facilities in Iraq, since the failure of the Mosul Dam could threaten the lives of large numbers of civilians and threaten U.S. personnel and facilities — including the U.S. Embassy in Baghdad."
It also noted that the failure of the dam could "prevent the Iraqi government from providing critical services" to the Iraqi people.
Some 1.5 million people have been displaced by fighting in Iraq since the Islamic State's rapid advance began in June. The scale of the humanitarian crisis prompted the U.N. to declare its highest level of emergency lasts week.
Associated Press writers Sinan Salaheddin in Baghdad, Lou Kesten and Robert Burns in Washington, Danica Kirka in London, and Andrea Rosa in Dahuk, Iraq, contributed to this report.