Italy's famed La Scala opera house has decided to return three million euros ($3.4m) in investment funding to Saudi Arabia after a plan to work closely with the kingdom was widely criticised by rights groups and the government.

Milan Mayor Giuseppe Sala, who also chairs La Scala's board, said the funds - part of a proposed 15 million euro ($17m) five-year partnership deal with the Saudi culture ministry - were deposited into an escrow account.

"Back to square one. We'll return the money to the Saudis," Sala told reporters on Monday, adding that the board voted "unanimously" to refund the down payment. "Right now, going down this road is not possible."

The proposed deal, which would have included giving a seat on the La Scala board to Saudi Arabia's Culture Minister Badr bin Abdullah, came under fire earlier this month in light of the country's human rights record.

The kingdom is under increased global scrutiny since the killing of a Saudi journalist Jamal Khashoggi inside its consulate in Istanbul last October and the plight of a Saudi woman who turned to social media to help escape alleged family abuse.

Deputy Prime Minister and Northern League leader Matteo Salvini had urged the opera house to reject the cash, while the governor of the Lombardy region - also a member of the Northern League - called for the dismissal of the opera house's artistic director, Alexander Pereira.

Sala said Pereira, who had negotiated the financing deal with the Saudi culture ministry, will keep his job.

'Not closing doors'

The fundraising deal foresaw the establishment of a music school run by La Scala's academy in Riyadh that would be open to all Saudi children regardless of gender.

While the current procedure aimed at making Saudi Arabia an official financial backer of the opera house was officially closed, Sala refused to rule out future talks with the kingdom.

He said a planned tour by La Scala's orchestra in 2020 will go ahead.

"We are not closing doors to Saudi Arabia," said Sala.

"It depends on the form of cooperation. We will do the tour. I wouldn't make a list of countries where it doesn't make sense to go. Also because this kind of activity can help in respect to the situation that exists today in Saudi Arabia."

Sala said the talks with Saudi Arabia, which included discussions before the gala season-opener on December 7, were poorly handled in terms of communication.

He said he had been aware of the talks, but not of their speedy advancement nor of the transfer of funds.

Other Western cultural institutes have also grappled with how to handle financial contributions from Saudi Arabia following Khashoggi's murder.

Earlier this month, a US-based talent agency, Endeavor, returned a $400m investment fund to Saudi Arabia and cancelled its contract.

Saudi Arabia, which has been making moves to open culturally to the West, participated for the first time in last year's Biennale architecture exhibit in Venice.

Italy is Saudi Arabia's ninth-largest trading partner, according to the Saudi embassy website.