A last-ditch effort to rescue a wayward whale that has transfixed Germans for weeks has begun in the Baltic Sea despite criticism it has little chance of success and could further harm the 12-tonne creature.

The male humpback whale was first spotted last month near Timmendorfer Strand on the northern coast of Germany, giving rise to its nickname Timmy. It has repeatedly become stranded and then freed itself after human assistance but it is now stranded again, with rescuers saying it is fighting a losing battle for its life.

But just as regional officials appeared ready to admit defeat and allow the stricken mammal to die, two multimillionaires came forward with funds to mount an 11th-hour rescue mission for which they won state approval.

One of the sponsors, Walter Gunz, the founder of a major electronics retailer chain, said that without the mobilisation, the whale would perish. “At least if you try something you have a chance of saving it,” he told the German news agency dpa.

Local media outlets have been running live streams about Timmy, who is 10 metres long, as emotions ran high. On Thursday they provided minute-by-minute coverage of what was being called Operation Cushion.

The long-shot scheme started when six helpers waded in hip-deep water to reach the animal. The silt beneath the whale’s flippers is to be flushed clear and the plan is then to slide air cushions under the animal to gently lift it on to a tarpaulin tethered to a pontoon on either side.

Should the team pull off this delicate task, Timmy would then be towed by tugboat out into the North Sea and possibly as far as the Atlantic Ocean in a final attempt to release it into more hospitable waters.

The mammal swam into the Baltic last month, possibly while chasing shoals of herring, which has far too little salt to sustain it. It reportedly also has wounds on its back and a skin infection.

The environmental pressure group Greenpeace, which had been involved in previous rescue attempts, criticised the current operation for the “sick and severely weakened” animal.

It cited reports from the German Oceanographic Museum and the Institute for Terrestrial and Aquatic Wildlife Research which suggested that the whale’s chances of survival were vanishingly low, while the mission involved a high risk of injury.

“We are now focusing our efforts on promoting the protection of the oceans, including as a habitat for whales,” a Greenpeace spokesperson said.

Critics said a closely fought race for an election in Mecklenburg-Western Pomerania, the state where the animal is stranded, in September appeared to be driving some of the official posturing.

The regional environment ministry said the scheme to save the whale, which is being co-financed by the equestrian event organiser Karin Walter-Mommert, bore full responsibility for the operation’s success or failure.

State-sponsored rescue efforts had already been suspended on 1 April. But the whale’s fight to cling to life inspired the public and mobilised a popular movement on its behalf.

On Wednesday, Till Backhaus, the environment minister for Mecklenburg-Western Pomerania, announced a U-turn in support of the “unique” rescue mission, saying he was “quite happy” about having a last chance at success.

“It’s not active, and it’s certainly not agile, but it still showing there’s life in it,” Backhaus said of the animal.

Frank-Walter Steinmeier, Germany’s president who was on a previously planned visit to the Baltic coast city of Stralsund on Thursday, organised a meeting with veterinary experts to discuss the animal’s plight.