Rock stars tethered their jet skis to the back of it during the film festival in Cannes, its clean lines have impressed quayside onlookers in Antibes, and England footballer Frank Lampard is reportedly set to propose to his television presenter girlfriend on board.

There can be no doubt that Roman Abramovich's enormous yacht Luna is enjoying the spotlight this summer as it tours the Mediterranean. But the citizens of Venice, a city more familiar than most with extravagant displays of wealth down the centuries, are not impressed.

The Russian oligarch's £115m, 377ft behemoth moored unannounced last week at one of the city's most stunning lagoon locations, as Abramovich and his girlfriend, Dasha Zhukova, pitched up for the Venice Biennale.

Local residents, accustomed to stunning views over St Mark's Basin, found themselves staring straight at the twin helipads and bulletproof windows of the vessel, which dwarfs all rival yachts at what has become an annual reunion of some of the most expensive private vessels in the world.

First to complain was Venice's mayor, Giorgio Orsoni, who is threatening a new tax on vessels such as the Luna. "The boats are getting too big and blocking the view," he said. "These yachts are showing up to see Venice for free, but St Mark's Basin is being turned into a motorway and we have to start limiting the traffic."

Marco Paolini, co-owner of the Caffè Florian on St Mark's Square, whose artsy customers launched the Biennale in 1895, condemned the "idiotic" presence of Abramovich's boat. "There are so many beautiful places here, why do these people have to bring their houses with them?" he said.

Complete with a covered pool, massive communications tower and a crew of 40, Luna is just one vessel in what has been dubbed Abramovich's "navy" of mega-yachts. Now moored at the Riva dei Sette Martiri, close to the Biennale Gardens, local bloggers have joked it could be mistaken for one of the more abstract installations at the show.

Abramovich, 44, has not been glimpsed amid the uproar. But Zhukova, 29, a noted party-thrower, has made the Luna the place to be seen for the critics, buyers and artists currently thronging Venice.

Elton John and Courtney Love were among the VIP crowd ducking in and out of the 89 national pavilions last week, with the longest queues at the British section, which has been given a makeover by installation artist Mike Nelson.

The boat, though unloved by locals who find themselves living temporarily in its shadow, has proved a celebrity magnet this summer, hosting singers Gwen Stefani and Gavin Rossdale at Cannes after Madonna's visit last summer. Reports have also suggested that Abramovich, the owner of Chelsea football club, could lend Luna to Lampard so he can propose to Christine Bleakley of ITV's Daybreak.

Severino Rigo, a retired IBM engineer who lives on the Riva dei Sette Martiri, said: "The real eyesores are the security barriers the crews erect where they dock, which extend out two to three metres across the pavement."

"I do not recall ever seeing such a large yacht as Abramovich's moored so close to the Biennale," said Enrico Tantucci, who is covering the event for local newspaper La Nuova Venezia. "It's like waking up in the morning to find someone has built an office block where the water used to be – no wonder locals have been complaining."

Zhukova's latest artistic project is also unlikely to endear her to Venetians. Many of the city's residents are embroiled in a battle to rid the city of the huge advertising hoardings that have been covering historic palazzi while they undergo restoration. The Coca-Cola billboard which engulfed the Bridge of Sighs and helped to spark the controversy is close to where the Luna is docked.

Zhukova has reportedly asked around 60 artists to create fake 15-second adverts which will be shown on a huge jumbotron TV screen, mounted on a barge sailing up and down the Grand Canal.

Zhukova has said she wants to open a debate about the anti-ad campaign, given that proceeds from the billboards are being used to pay for the vital restoration of Venice's palazzi.

The arrival of the mega-yachts has also exacerbated tensions over the rapidly growing number of cruise ships which steam past St Mark's and down the Giudecca canal before dropping off thousands of passengers who "just have time to eat a frozen lasagna and look for a place to pee", according to one of the signatories to the growing Facebook campaign to stop the 50ft-tall cruisers they claim shake the foundations of Venice's ancient buildings.

Rigo said that the hundreds of cruise ships now filing past his window were an even bigger problem than the mega-yachts. "After all, the private boats represent high-quality tourism," he said.

Not everyone is so negative. Abramovich's huge wealth has become a crucial asset to the Biennale which, held every two years, has become the world's most important contemporary art event. His funding has prompted new competitions and collections. Franca Coin, president of the Venice Foundation, said residents should be grateful to Abramovich and Zhukova for patronising the arts. "One more yacht in Venice is a lesser evil," she told Corriere della Sera.

Zhukova, the daughter of a Russian tycoon, has made a substantial impact in the art world, successfully opening Moscow's first modern art gallery in a former bus depot, while helping her boyfriend in plans for a $400m arts complex on an island he is leasing in St Petersburg.

But for Rigo and his neighbours, support for the arts only partly compensates for the blight of so many gleaming trophies of the super-rich 20 metres from his front door: "The vessels only stay a few days, but I'd rather see the beautiful view from my window, and the tourists don't know what they're missing."

• This article was amended on 5 June 2011 to correct the impression that Zhukova spoke to Italian media about the anti-ad campaign. She told the Wall Street Journal.