A wayward humpback whale and her calf who turned the wrong way in San Francisco bay a week ago and ended up 90 miles inland have turned back towards the Pacific Ocean, the US Coast Guard said.

The plight of the two whales has captured the imagination of Californians, who have crowded onto the banks of a waterway by Sacramento as marine biologists try to coax them back towards safety.

Initially, rescuers tried to lure the pair downstream by playing recordings of humpbacks feeding, to no avail. But the pair surprised the experts yesterday, when they started to swim back to the southwest from the California state capital.

Jim Oswald, of the Marine Mammal Centre, said that they appeared to have followed a group tugboats, possibly drawn by the sound of their engines.

But Carrie Wilson, a marine biologist with the California Department of Fish and Game, gave warning that the pair still had miles to go and many obstacles to overcome on their route from the Sacramento-San Joaquin Delta to the Pacific, down rivers and a man-made canal.

Nicknamed Delta and Dawn, the humpbacks started moving toward the Pacific yesterday afternoon, swimming at about 6 mph towards San Francisco. They are believed to have been injured already by a boat's propeller and as darkness fell, Coast Guard vessels stopped following them to avoid another accident.

Ahead of the pair lie muddy swamps and deltas in which they could be trapped. They will also have to make their way between the pylons of four bridges before they reach San Francisco Bay, after which they would swim under the Golden Gate Bridge to freedom.

During their journey, boats will be positioned at the mouths of tributaries where the whales could possibly go off course.

“We’ve got a bunch of metal pipes and hammers, and if we need to we can give the other boats pipes to bang on to persuade the animals not to turn in the wrong direction,” said Ms Wilson.

Despite their brush with the boat, the whales appear to be in good health and were swimming at a steady pace, officials said.

Among whaling experts joining the rescue effort was Bernie Krause, an electronic audio specialist known as the "whale whisperer”.

Mr Krause lowered loudspeakers into the water and played recorded whale noises as he did during the successful 1985 rescue of another humpback whale who followed a similar route. That whale, nicknamed Humphrey, survived 26 days before he was eventually lured to safety.

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