The US-backed anti-Daesh coalition said it was unable late Saturday to confirm the report.
Iraqi TV said Al-Jumaili was killed with other Daesh commanders in a strike carried out by the Iraqi air force in the region of Al-Qaim, near the border with Syria.
“The air force’s planes executed with accuracy a strike on the headquarters of Daesh in Al-Qaim ... resulting in the killing of Daesh’s second-in-command ... Ayad Al-Jumaili, alias Abu Yahya, the war minister,” said state TV, citing a statement from the directorate of military intelligence.
US and Iraqi officials believe Al-Baghdadi has left operational commanders with diehard followers to fight the battle of Mosul, and is now hiding out in the desert with senior commanders.
A separate battle is in preparation in Syria to drive Daesh from its stronghold there, the city of Raqqa.
The Iraqi state TV report is the first by an official media to announce the death of Al-Jumaili, who was an intelligence officer under Saddam Hussein, the Iraqi president toppled in the 2003 US-led invasion.
Al-Jumaili led Daesh’s top security agency in Iraq and Syria, known as Amniya, answering directly to Al-Baghdadi, according to experts.
Meanwhile, in a muddy camp in northern Syria, civilians who fled Raqqa said fear of an expected US-backed assault on the Daesh bastion was reaching a fever pitch.
This week, hundreds of civilians escaped Raqqa and headed north to the camp in Ain Issa, in territory controlled by the Syrian Democratic Forces (SDF), a US-backed Arab-Kurdish alliance.
As part of their campaign to capture Raqqa, the SDF has been bearing down on the Daesh-held town of Tabqa and the nearby vital Tabqa Dam over the past 10 days.
Rumors that Syria’s biggest dam would collapse and flood Raqqa, 55 km downstream, have sparked panic in the city.
“The hisbah (religious police) announced over the megaphones ‘the land of Muslims will be flooded, the Tabqa Dam has collapsed’,” said Mohammad Mahmoud, 38.
Mahmoud, his brother and both their families paid $1,000 to a smuggler and fled Raqqa on foot earlier this week. “It’s hell there. Fear rules over everything,” he said as he took apparent pleasure puffing on a cigarette.
Coalition airstrikes against Daesh have likely “unintentionally” killed 229 civilians since the offensive began in 2014, according to US Central Command.
The tally does not include civilian casualties from March — which could include potentially large numbers of civilians killed in strikes over several days in Mosul’s Al-Jadida area. Attention has focused on one allegedly particularly deadly strike on March 17.
Separately, Turkey’s foreign minister said tens of thousands of displaced Syrians and refugees have returned to an area controlled by Turkey and Turkish-backed opposition fighters in northern Syria.
Turkish Foreign Minister Mevlut Cavusoglu’s comments came three days after Prime Minister Binali Yildirim said Turkey’s Operation Euphrates Shield that began in August had ended after its troops and allied fighters secured territory along the border between Turkey and Syria.
Cavusoglu said some 50,000 people have returned from Turkey to areas that have been captured by Turkish troops and Turkey-backed opposition fighters, adding that security in these areas should eventually be handed to local forces.