German federal prosecutors announced Tuesday a probe into Hamas on suspicion of kidnap and murder of German citizens following the militant group's weekend assault on Israel.

Prosecutors "have opened an investigation against unidentified members of the radical Palestinian Islamist organization Hamas," a spokeswoman for the federal prosecutor's office told AFP.

The probe is over suspicions "of belonging to a foreign terrorist group, hostage-taking and murder", she said.

Dozens of foreigners have been killed, injured or taken hostage during the attack by Hamas.

A foreign ministry source in Berlin earlier said that several Germans who are also Israeli nationals were among those kidnapped by Hamas militants, without giving an exact number.

Chancellor Olaf Scholz said Berlin was working "intensively" with Israel to learn the fate of German citizens among the hostages, "how many people it is and what we can do to secure their freedom".

One German-Israeli woman, 22-year-old Shani Louk, is believed to have been abducted when militants attacked a rave party in the desert near the border with the Gaza Strip, according to her mother.

In a video on broadcaster ARD Tuesday, the mother Ricarda Louk said she had received new information that her daughter was "alive but has a severe head injury and is in critical condition.

"Every minute is critical, and we are asking the German government to act quickly."

Media reports have said a 22-year-old female student from Berlin, who was on holiday in Israel, was killed at a kibbutz close to Gaza.

German authorities have declined to make any comment on cases of Germans killed in the conflict.