By Ali Abdelaty

CAIRO (Reuters) - Egyptian President Abdel Fattah al-Sisi told the interior minister on Friday to crack down on police abuse and to submit proposals to parliament to achieve this goal, the presidency said, as anger mounts over alleged police brutality.

Their meeting came a day after a police officer shot dead a man in the street, angering hundreds of people who protested in front of the Cairo security directorate.

The policeman had attacked a driver after an argument and was forced to flee a mob of local people who attempted to lynch him, said a statement from the directorate. The policeman was later arrested.

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.

Sisi told Interior Minister Magdi Abdel Ghaffar tackle abuses and propose any necessary amendments to laws within 15 days, the presidency said in a statement.

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

Since then, police have regained their power and human rights groups allege they often act with impunity. The Interior Ministry denies the accusations and says it investigates any violations.

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, but the incident has put a fresh spotlight on Egypt's human rights record.

Earlier on Friday, the state news agency quoted Interior Ministry spokesman Major General Abu Bakr Abdel Karim as saying policemen are not shielded from the law.

SISI'S POPULARITY DIMINISHES

As army chief, Sisi toppled Islamist Mohamed Mursi -- Egypt's first freely elected president -- in 2013 after mass protests against his rule.

The toughest crackdown on dissent in Egypt's modern history followed. Security forces killed hundreds of Mursi supporters at a protest camp in one day. Thousands of other Islamists were jailed. Later, liberal activists were rounded up.

Sisi was elected president, promising stability after years of political turmoil caused by the 2011 revolt. But he no longer enjoys his once cult-like following.

Egyptians are frustrated over issues that successive leaders have failed to tackle: the alleged police abuses, unemployment, dilapidated infrastructure and corruption.

In recent weeks, imported commodities like cooking oil have been scarce as a dollar shortage makes it harder for state importers to secure regular supplies.

Affordable food is an explosive issue in Egypt, where millions live a paycheck from hunger, and economic discontent helped unseat two presidents in five years.

(Writing by Michael Georgy; editing by Katharine Houreld)