St. Mark's Square in Venice was awash with water and closed on Sunday as city authorities managed another exceptional high tide just days after devastating flooding.

Venice, beloved around the world for its canals, historic architecture and art, suffered its worst flooding in 50 years on Tuesday.

Another historic high tide hit at midday on Sunday — the third time in one week that water levels passed 150cm.

The mayor of Venice, Luigi Brugnaro, said on Saturday the city was "on its knees."

However, he said the situation was not expected to be as bad as on Tuesday, when the flooding inundated squares, shops, homes and hotels.

Brugnaro, who has been appointed special commissioner to deal with the inundation, estimated damages from the flooding in the city since Tuesday at around 1 billion euros.

The Teatro La Fenice's electrial system has been damaged, which may affect the upcoming season. Workers are now busy repairing it and opera rehearsals have to be carried out in other theatres.

Volunteers in Venice have been working to save ancient music scores and books stored in the Benedetto Marcello Conservatory. It has asked for help on social media to salvage items after severe flooding.

On Tuesday, the tide peaked at 187cm, just short of the record 194cm set in 1966. In normal conditions, tides of 80-90cm are generally seen as high but manageable.

Authorities in Florence and Pisa were also closely monitoring the Arno river, whose water levels rose rapidly in the night due to heavy rain.

Italy's longest river, the Po, which runs across northern Italy passing through Turin, was also being monitored after its level rose by 1.5 metres in the last 24 hours due to heavy rain.