German prosecutors have launched an investigation into the suspect in the deadly gun attack at a Christmas market in eastern France, a spokesman for the service said Thursday.

Cherif Chekatt, 29, is under investigation for alleged murder, attempted murder and grievous bodily harm, Markus Schmitt, a spokesman for German prosecutors said, confirming a report in the Tagesspiegel daily.

The German probe runs in parallel with the French investigation, Schmitt added.

Chekatt was jailed for burglary in Germany in 2016 but was not deemed a potentially dangerous militant, German authorities said Wednesday.

Even though Tuesday evening's attack took place on French soil, several German nationals were present at the site during the assault. They were not wounded but they suffered shock.

The gunman opened fire at the famed Strasbourg Christmas market, which draws thousands of visitors every year.

The attack left three dead and 13 injured, according to the latest toll given by the French authorities.

German police have tightened border checks over fears that the suspect may have crossed over from neighbouring France.