Prosecutors investigating the driver of a car that ran over and fatally injured an Egyptian woman in eastern Germany say they are also now pursuing a man who witnesses say hurled racial abuse at the victim after the accident.

The 22-year-old student, identified only as Shaden M., died in hospital on April 18, three days after the accident in the city of Cottbus, and the driver is being investigated for possibly causing death by negligence, Horst Nothbaum, spokesman for the prosecutor's office, said.

Two witnesses came forward 10 days after the accident to say that they had heard a passenger in the car that struck the woman yelling insults afterwards, including: "Go back to where you came from, then you won't get run over. Damn refugees."

Nothbaum said a new investigation of possible incitement to racial hatred was launched on Wednesday.

Germany has seen a sharp increase in anti-immigrant rhetoric after the influx of over a million migrants over the past two years, and officials say the growing right-wing extremist scene is also increasingly willing to commit violence.

Nothbaum said there was no suggestion that the car had deliberately run over the woman. He said witnesses to the accident said it happened when she stepped off a curb into traffic in the center of the town, near a streetcar stop.

Martina Muench, education minister in the state of Brandenburg that includes Cottbus, welcomed the investigation, and said foreign students, teachers and researchers helped strengthen the competitiveness of the state.

"It would be a shame if these allegations are proven true," Muench said in a statement. "It is unfathomable and appalling that a young, fatally injured woman would be insulted in such a racist and xenophobic way in the middle of Cottbus."

The state education ministry said international students accounted for about 7,800, or just over 16 percent, of the state's 48,000 students, and around 620 of the state's academic staff came from overseas.