“The competent authorities have been able to retrieve a first tranche amounting to 182.6 billion Iraqi dinars,” Mr Al Sudani said in a televised speech, surrounded by piles of Iraqi and US banknotes.
He called on those responsible to hand themselves in.
The scandal — revealed last month and labelled the “heist of the century” — involved 3.7 trillion Iraqi dinars ($2.5 billion) fraudulently paid to five companies by the General Commission of Taxes.
The money was paid through 247 cheques between September 9, 2021, and August 11 from the commission's account at the state-run Rafidain Bank.
Since then, an investigation has been under way. A number of government officials and two businessmen have been arrested and some of the money recovered, although no senior politicians have faced official accusations.
UK newspaper The Guardian claimed last week that a former commission director and other employees played a key role in the theft, backed by Iran-aligned party Badr Organisation.
A Finance Ministry official involved in the investigation told The National that the investigation has yet to uncover involvement by a senior political figure or party.
But he would not rule anything out.
“Of course, in a heist that big there is someone influential behind it but we can’t point a finger at this stage,” he said, requesting anonymity.
The Badr Organisation, which is headed by influential politician Hadi Al Amiri, controls senior appointments in the tax and customs commissions, according to the sources mentioned by The Guardian.
All the money came from businessman Nour Jassim, 42, the chief executive of Al Qanit and Al Mubdioon companies, who was arrested last month, Mr Al Sudani said. He was arrested at Baghdad International Airport as he was trying to leave the country on a private jet.
The businessman confessed that he had received more than $1 billion, Mr Al Sudani claimed.
In a compromise with the court, he was released on bail on condition of recovering the remaining funds within two weeks, the Prime Minister added.
“Arresting the thieves and those who aided them is very important,” he said.
“But the most important thing is the return of the funds. What does it matter if so and so is in prison if the [$2.5 billion] is not in the state's coffers?”
Another businessman, identified by Mr Al Sudani as Hussein Kawa Abdul Qadir, has been arrested by authorities in the semi-autonomous Kurdish region in northern Iraq.
“We call upon all the suspects subject to arrest warrants in this case to hand themselves in and hand back the stolen funds,” the Prime Minister said.
Some Iraqis mocked Mr Al Sudani's speech, describing it as a farce and criticising him for freeing Mr Jassim.
“Releasing Nour on bail is a catastrophe in the fight against corruption,” politician Youssif Al Kilabi said.
Fellow politician Bassim Khashan said the speech was merely “a show”, and also condemned the release of the businessman.
He said Mr Jassim's release was “only to sell properties that have been seized by the court in order that the thief can kindly return some the money he stole from the state”.
This is one of the country's biggest corruption-related scandals since the 2003 US-led invasion that toppled Saddam Hussein’s regime, and has led to widespread anger in Iraq.
The country was ranked 157th out of 180 countries on the 2021 corruption index by the global watchdog Transparency International.
Mr Al Sudani, who took office late last month, has vowed to crack down on corruption but few expect any senior officials or political leaders to be held accountable.