Days after an attacker driving an S.U.V. killed five people at a Christmas market in eastern Germany, calls for solidarity have given way to political sniping, as questions grew on Monday about the authorities’ inability to prevent the deaths.

The police are holding a Saudi refugee, a 50-year-old doctor, who they say carried out the attack. His detention brought concerns about immigration and security back to the fore, with political leaders on Monday looking to position themselves on those hot-button issues ahead of snap elections scheduled for February.

Despite calls not to use the attack for political purposes, criticism of the German government — including from Elon Musk — has cropped up from all sides. The fallout looks likely to supercharge what was already shaping up to be a brief, intense campaign following the collapse of the government after Chancellor Olaf Scholz lost a confidence vote in Parliament last week.

The hard-right Alternative for Germany party called for a demonstration on Monday in Magdeburg, the town where the attack took place, to mourn the victims. But in a social media post, the party’s candidate for chancellor, Alice Weidel, made clear that the event would also be used for political purposes.

“Magdeburg would not have been possible without uncontrolled immigration,” said Ms. Weidel, whose party has been polling in second place in recent months, behind the conservative Christian Democrats. She added, “The state must protect its citizens through a restrictive migration policy and consistent deportations!”

The attacker in Magdeburg plowed an S.U.V. into the city’s main Christmas market on Friday, killing a 9-year-old boy and four women, the police said, and wounding more than 200 others. As more indications have emerged that the authorities had been alerted to the erratic behavior of the suspect, demands have also increased for answers to why the warnings were not taken more seriously.