Germany's president said on Tuesday that a deadly car-ramming attack on a Christmas market had cast a "dark shadow" over this year's celebrations but urged the nation not to be driven apart by extremists.

In his traditional Christmas address, President Frank-Walter Steinmeier sought to issue a message of healing four days after the brutal attack in the eastern city of Magdeburg killed five people and left over 200 wounded.

"A dark shadow hangs over this Christmas," said the head of state, pointing to the "pain, horror and bewilderment over what happened in Magdeburg just a few days before Christmas".

He made a call for national unity as a debate about security and immigration is flaring again: "Hatred and violence must not have the final word. Let's not allow ourselves to be driven apart. Let's stand together."

His words came a day after the far-right Alternative for Germany (AfD) held what it called a memorial rally for the victims in Magdeburg, where one speaker demanded that Germany "must close the borders".

Nearby, an anti-extremist initiative was held under the motto "Don't Give Hate a Chance".

Steinmeier recognised that there was a "great deal of dissatisfaction about politics" in Germany but insisted that "our democracy is and remains strong".

A Saudi doctor, Taleb al-Abdulmohsen, 50, was arrested Friday at the scene of the attack in which a rented SUV ploughed at high speed through the crowd of revellers, bringing death and chaos to the festive event.

His motive remains unclear.

Abdulmohsen has in his many online posts voiced strongly anti-Islam views, anger at German authorities and support for far-right conspiracy narratives on the "Islamisation" of Europe.

The Saudi suspect has been remanded in custody in a top-security facility on five counts of murder and 205 of attempted murder, prosecutors said, but not on terrorism-related charges. (AFP)