Venice authorities have called on people around the world to help restore the stricken lagoon city following a series of devastating floods.

The mayor, Luigi Brugnaro, has opened a bank account for contributions, writing on social media that Venice is “the pride of Italy and everyone’s heritage”. “Thanks to your help, it will shine again,” he added.

It will take billions of euros to achieve that aim. The Unesco world heritage site was brought to its knees by the worst flood since 1966 last Tuesday night, severely damaging homes, shops, restaurants, museums and monuments, including the 1,000-year-old St Mark’s Basilica. The acqua alta, or high water, returned on Wednesday and Thursday before another deluge on Friday. Yesterday St Mark’s Square reopened, but the city forecast high water of 160 centimetres (more than 5ft) for today, lower than Tuesday’s high of 187cm but still dangerous. The full cost of the flooding, which also wreaked havoc on other islands in the lagoon, including Murano and Pellestrina, where two people died, has yet to be assessed, but the first flood alone caused an estimated €1bn of damage.

Pino Musolino, president of the north Adriatic port authority, has written to the bosses of cruise ship companies serving the lagoon, urging them to help Venice “overcome this tragedy”. The massive cruise liners are hugely unpopular with residents, with most wanting them banned from the lagoon, but the cruise sector also supports 4,500 jobs in Venice.

“It would be a message of great importance on your part and on the whole cruise line if you decided to raise funds to support our stricken city and its inhabitants,” Musolino wrote in the letter. “It would also be a tangible sign of your closeness to Venice and a concrete sign that it is possible to build a trusting relationship between the cruise industry and the Venetian community.”

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Meanwhile the cultural world is rallying in support, with Milan’s opera house, La Scala, pledging to raise funds for its counterpart in Venice, the Teatro La Fenice, forced to close days before the beginning of the opera season after water flooded its control room, where its electrical and fire-prevention systems are located.

“All the artists, workers and management of La Scala were deeply shocked by the images of one of the most beautiful cities in the world submerged by high water with few precedents in history,” said Alexander Pereira, the opera house’s outgoing chief executive and artistic director.

City residents have proposed fresh initiatives to raise funds, including Ewa Gorniak Morgan, a writer and translator who has lived in Venice since 1995 and has suggested that social media firms find a way in which those who post photos of the city on their sites can donate a nominal sum of 10 cents or €1. In return, each photo with a donation would be distinguished with a small heart and the slogan: “Venice my love”.

Facebook Twitter Pinterest A woman sits in a flooded St. Mark’s Square. Photograph: Luca Bruno/AP

“The image of Venice, sadly and undoubtedly the most popular on social media and other media channels these days, is universally recognised and it is through this image that a worldwide awareness can be created and financial help can be obtained,” Morgan wrote in a statement to the press.

Venetians usually shrug their shoulders when asked about acqua alta, saying they are used to it. But this time it is different. As they assess the ramifications of the latest floods, anger is mounting over the authorities’ persistent failure to protect the city. “We are worried because people are starting to be desperate,” Cardinal Francesco Moraglia, the patriarch of Venice, said on Friday.

“These phenomena – that we are used to living with – are now becoming disruptive.”