The humpback whale that freed itself early on Friday from a sandbank off of Germany's Baltic Sea coast is now heading out of the Bay of Lübeck, a marine scientist said.

Stephanie Gross from the Institute for Terrestrial and Aquatic Wildlife Research (ITAW) said the marine mammal was on course to leave the bay.

A colleague of hers was in an inflatable boat directly alongside the 12 to 15-metre-long whale, which is also being accompanied about 300 metres off the coast by a coastguard vessel and several boats, Gross said.

No transmitter was attached to the whale because its skin was too badly diseased.

The whale was stuck in shallow waters off Timmendorfer Beach since early on Monday, drawing heavy media attention.

What matters now is that the whale stays in open water and swims into the North Sea if possible, biologist Robert Marc Lehmann said.

But the large mammal is still not home free, as its release from the sandbank is not a rescue but only a small step in the right direction, he said. It would only be home once it reached the Atlantic, Lehmann added.

Lehmann said the whale had been able to swim into deeper water through a channel dug out by a floating excavator. The biologist had snorkelled out to the whale on Thursday and tried to guide it through the trench.

Politicians had pledged help

"I am simply just glad," said the mayor of Timmendorfer Beach, Sven Partheil-Böhnke. Schleswig-Holstein Premier Daniel Günther also expressed his joy at the rescue and thanked the volunteers on site, WDR public broadcaster reported.

Günther had pledged the state’s support after visiting the site to assess the situation. Ahead of the whale’s release, he told a dpa reporter that the northern German state would provide up to two boats to help guide the animal through the Baltic Sea and prevent it from running aground again.

He reiterated that offer on Friday.

"Let's see whether we have to accompany it and help it out. We offered it, but for now [the whale] can no longer be seen on the beach," Günther said, adding that the priority was for the marine mammal to find "the right way" out.

Whale fought through dug trench

For Timmendorf on the Baltic Sea coast, the unprecedented multi-day rescue operation involving excavators and divers has thus come to a happy ending.

Efforts to free the whale had continued for days. An initial attempt using a small suction dredger failed on Tuesday. On Thursday, rescuers dug a trench with a floating dredger to create a path back to deeper water.

Metre by metre, the whale moved through the channel on Thursday evening. A larger excavator was later brought in from land after an embankment was built to allow the heavy machinery to reach the site.

The animal appeared more active than in previous days. In the evening, helpers also tried to encourage it with noise - by honking, drumming or shouting. The animal itself also repeatedly emitted a loud humming sound.

By nightfall, only a few metres remained to deeper water, Mayor Partheil-Böhnke said, but the operation was suspended due to darkness. Overnight, the whale managed to free itself.

Not native to the Baltic Sea

Why the whale had appeared off the coast is still unclear. Gross from the ITAW had said that perhaps the animal was ill or injured or perhaps simply exhausted. It is also possible that it entered the shallow waters by chance.

The marine conservation organization Sea Shepherd believes the animal is probably the same whale that had previously been repeatedly sighted off the coast of Mecklenburg-Vorpommern in early March, when it appeared in the Wismar harbour and and caused a stir.

Large whales such as humpbacks are not native to the Baltic Sea. In search of food, they may follow shoals of fish into the area. Experts say underwater noise could also be a contributing factor.