CAIRO (Reuters) - Egyptian President Abdel Fattah al-Sisi said he would ask parliament to amend the law to toughen sanctions for police abuses, his office said Friday, a day after an officer shot dead a driver.

The statement from his office came as dozens of demonstrators gathered outside Cairo police headquarters chanting: "The interior ministry are thugs," after the officer killed the driver over a fare dispute.

Egypt's Interior Ministry also said on Friday that any policeman who violates the law will be prosecuted.

Interior Ministry spokesman Major General Abu Bakr Abdel Karim was quoted by the state news agency as saying policemen are not shielded from the law.

Hundreds of protesters gathered in front of the Cairo security directorate on Thursday night after the man was killed.

A statement from the directorate said the policeman had shot dead a driver after an argument and was forced to flee a mob of local people who attempted to catch and kill him. Police later found the policeman.

Footage posted on social media showed hundreds of people massing outside the security directorate to protest the death.

The incident comes amid mounting public anger over alleged police brutality. Last week, thousands of doctors held a rare protest against police they say beat two doctors at a Cairo hospital for refusing to falsify medical records.

Earlier this month, the body of a missing Italian graduate student was found on the outskirts of Cairo showing signs of torture, including electrocution. Activists said the injuries had the hallmarks of Egyptian security services. The Interior Ministry has denied allegations of involvement in the death.

The Interior Ministry has denied allegations by human rights groups that police commit widespread human rights violations and has vowed to punish any violations.

Anger over perceived police excesses helped fuel the 2011 uprising that ended President Hosni Mubarak's 30-year rule. The protests began on a Police Day holiday.