Robbers made off with three priceless diamond sets from a state museum in Dresden on Monday, police and museum directors said, in what German media have described as the biggest art heist since World War Two.

The thieves broke into the Green Vault at Dresden's Royal Palace -- home to around 4,000 precious objects of ivory, gold, silver and jewels -- at dawn after a power cut deactivated the alarm.

The stolen items included brilliant-cut diamonds that belonged to a collection of jewellery of 18th-century Saxony ruler Augustus the Strong.

"We are talking here about items of inestimable art-historical and cultural-historical value," the director of Dresden's state art collections Marion Ackermann told reporters at a press conference on Monday.

"We cannot put an exact value on them because they are priceless," said Ackermann, adding she was "shocked by the brutality of the break-in."

The thieves launched the brazen raid after a fire broke out at an electrical panel near the museum in the early hours of Monday, deactivating its alarm as well as street lighting, police said, adding that investigations were ongoing to determine if there was a link to the robbery.

Despite the power cut, a surveillance camera kept working and filmed two men breaking in.

They smashed a window and cut through a fence before making their way to a display case "in a targeted manner" and destroying it, the head of

Dresden police Volker Lange said.

They remain on the run.

Bild daily said the heist was "probably the biggest art theft since World War Two".

Dirk Syndram, director of the Green Vault itself, said the museum's jewellery sets amounted to "a kind of world heritage", totalling about 100 items.

He explained that the stolen sets were part of a ten-set collection which includes not only diamonds, but also sapphires, rubies and emeralds.

Founded by Augustus the Strong, Elector of Saxony in 1723, the Green Vault is one of 12 museums which make up the famous Dresden State Art Collections.

 One of the oldest museums in Europe, the Green Vault holds treasures including a 63.8-centimetre figure of a Moor studded with emeralds and a 547.71-carat sapphire gifted by Tsar Peter I of Russia.

The museum is now made up of two sections -- a historic part and a new section.

Monday's raid targeted the historic section, which contains around three-quarters of the museum's treasures and which has a strict limit on the number of daily visitors.

Exhibits are arranged into nine rooms, including an ivory room, a silver gilt room and the central "Hall of Treasures".

One of its most valuable pieces, the green diamond, is currently on loan to the Metropolitan Museum of Art in New York, where it is a headline attraction in the temporary exhibition "Making Marvels: Science and Splendor at the Courts of Europe".

After the Royal Palace suffered severe damage in World War Two, the Green Vault remained closed for decades before it was restored and re-opened in 2006.

Saxony's state premier said the heist went beyond the value of the artefacts stolen.

"The treasures that are found in the Green Vault and the Dresden Royal palace were hard-earned by the people of Saxony over many centuries," Michael Kretschmer said.

"One cannot understand the history of our country, our state without the Green Vault and Saxony's State Art Collections."

In 2010, the museum hosted a meeting between Chancellor Angela Merkel and then President of the United States Barack Obama, on the latter's first state visit to Germany.

The museum remained closed and sealed off by police on Monday.

Monday's theft is the second high-profile heist in Germany in recent years, after a 100-kilogramme (220-pound), 24-karat giant gold coin was stolen from Berlin's Bode Museum in 2017.

Dresden police said they were in contact with colleagues in Berlin to examine "if there are any connections and if there are similar patterns in the crimes".

Germany's culture minister Monika Gruetters said that protection of museums and cultural institutions was now of "the highest priority".

 "The theft of items which make up our identity as a nation of culture strikes at our hearts," she said.