LISBON (Reuters) - A legal probe that led to the resignation of Portugal's former premier and soon-to-be EU Council leader is ongoing, the country's attorney general said late on Monday, adding she does not know when it will end.

Antonio Costa, 62, stepped down as premier last November over an investigation by the Portuguese public prosecutor's office into alleged illegalities in his government's handling of several large investment projects.

The prosecutors' case has largely fallen apart after judges at Lisbon's Court of Appeal and Portugal's ombudswoman said the investigation was based on speculation, not evidence.

Costa has denied wrongdoing, was never charged with a crime and will succeed Belgium's Charles Michel as the next president of the European Council, despite fears the investigation could jeopardise his ambitions for a EU top job.

In a rare interview with public broadcaster RTP, Attorney General Lucilia Gago said prosecutors do not need strong evidence to investigate and that they have the obligation to do so regardless of the person suspicions fall on.

"There is no one above the law," Gago said.

Even though Lisbon's Court of Appeal said there was no strong evidence of wrongdoing, Gago said the investigation remained open and was ongoing.

"I don't know how long it (the investigation) will take, nor the result," Gago said. "What I want to emphasise is the investigation continues...If the investigation has not closed, it is because something is preventing it (from closing).

Gago said it was unlikely there was an error as the prosecutors in charge of such investigations had high level of expertise and handled all evidence available with "great care".

Since Costa's resignation, which triggered an election in March, prosecutors have faced criticism for allegedly investigating him without having a watertight case. A judge has dropped the corruption charges against several people who were formally accused.

(Reporting by Catarina Demony and Sergio Goncalves; Editing by Christina Fincher)

By Catarina Demony and Sergio Goncalves