Egypt's President Abdel-Fattah el-Sissi has for the first time spoken publicly about the recent shooting death of a female protester, offering condolences to her family and all Egyptians "pained" by her death.

Shaimaa el-Sabbagh, a 32-year-old mother and activist, was killed 10 days ago while taking part in a peaceful protest in Cairo. Activists and witnesses at the rally blame the police for her death.

Egyptian state media on Monday quoted el-Sissi as saying he views Egyptian men and women as his own children and that el-Sabbagh "is my daughter ... no one should doubt that."

Egypt's top prosecutor has ordered an investigation into the killing and Interior Minister Mohammed Ibrahim, who is in charge of police, said he would personally hand over any force member found to be involved.