Dietrich who aroused anger in Germany for backing the Allies during World War II began as a cabaret singer in the 1920s before she became a Hollywood star and later returned to the stage as a singer.
Born in Berlin on December 27, 1901, she died in Paris as a recluse in 1992, and was buried in Berlin.
"She was an extraordinary artist who had a following around the world," President Rau said. His office placed a wreath on her grave on Thursday. "She also worked actively for democracy and freedom during the era of the Nazi dictatorship."
"Dietrich was far ahead of many of her contemporaries," the mayor's chief of staff, Andre Schmitz, said.
Dietrich, who left Germany for the United States in 1930, turned her back on Germany after Adolf Hitler rose to power three years later, rejecting approaches from the Nazis to return. She became a U.S. citizen in 1939, and sang for American troops as they fought her countrymen.
"Hitler is an idiot," she said in a wartime interview broadcast from Britain into Germany. "Boys, don't sacrifice yourselves. The war is crap and Hitler's an idiot."
"She didn't betray the real Germany by doing that," Schmitz said.
"She was the most passionate and erotic woman of the 20th century," said actress Ute Lemper who plays Dietrich in a local theatre production. "The animosity she faced after the war showed that not everything was okay in Germany back then."
Dietrich received a frosty reception when she returned to Berlin for a concert in 1960, facing protests with some demonstrators spitting at her and waving posters saying "Go Home Marlene."
The always charismatic Dietrich nevertheless got a roaring reception inside the packed theatre, taking 18 curtain calls.
The blonde diva's husky voice, high cheekbones, and gloriously long legs entranced audiences for decades after her breakthrough as a sultry cabaret singer in the 1930 film "The Blue Angel."
That and many of her other films are being shown in Germany this week. Museum exhibits, musical galas and documentaries also pay tribute to Germany's only film goddess.
Even though she returned to Germany only twice after the war in 1947 for a film and the infamous 1960 concert Dietrich nevertheless chose Berlin as a final resting place after the 1989 fall of the Berlin Wall.
Dietrich's burial in Berlin in 1992 was marked by controversy and an official civic ceremony was cancelled because of the lingering resentment. In recent years, Dietrich's grave in Berlin was desecrated by vandals. Police once found the words "fur-wearing slut" daubed in red paint on her gravestone.
Attempts by some local fans in her hometown district of Schoeneberg to rename a section of the street she was born on into "Marlene-Dietrich-Strass" were blocked in 1996 by resistance from die-hard opponents.
Werner Gephard, a retired banker visiting the grave, said he was a lifelong Dietrich fan and believed the animosity was gone.
"She was a fantastic actress and every man's dream," said Gephard, 71. "She always fascinated me. The incorrigibles are all gone by now."
©MMI CBS Worldwide Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. Reuters Limited and the Associated Press contributed to this report