BERLIN — Two days after a right-wing politician was assaulted in Germany, drawing international attention, the authorities on Wednesday said that several elements of the account given by his political party appeared to be false.

Frank Magnitz, 66, a member of Parliament from the Alternative for Germany party, suffered head injuries in the attack in Bremen on Monday. Party officials said that three men had attacked him, beating him with a piece of lumber and then kicking him after he had fallen to the ground.

But after reviewing a video of the attack, law enforcement officials said that one assailant had struck Mr. Magnitz once from behind, knocking him down, before he and two others fled the scene.

No one hit the lawmaker with an object, they said, and no one kicked him.

“We assume that all of the injuries are the result of the fall,” said Frank Passade, a spokesman for the state’s attorney’s office in Bremen, which is investigating the assault.