Authorities had tightened security in Cairo and other cities after Islamists called for protests against the government of President Abdel Fattah al-Sisi, the former army chief who ousted his Islamist predecessor Mohamed Morsi in 2013.
Demonstrators, mostly Islamist backers of Morsi, clashed with police, leaving 12 protesters dead in Cairo and another in the Mediterranean city of Alexandria, a health ministry official told AFP.
Officials said the protester in Alexandria was shot dead by police after he opened fire on them.
Hundreds of other protesters who denounced both Islamists and the government also clashed with police in central Cairo.
The interior ministry said protesters shot dead a police conscript in the clashes in two north Cairo neighbourhoods that are strongholds of Islamist protests. Three other officers were wounded.
At least 150 people were arrested across the country as police dispersed protests which saw many leftwing demonstrators also participating, security officials said.
In downtown Cairo, police fired shotguns and tear gas against hundreds of protesters who tried to march on the central Tahrir Square, the epicentre of the early 2011 revolt that ousted Mubarak.
Armoured vehicles were stationed around Tahrir, but despite extra security in the capital jihadists managed to set off a bomb in Cairo that wounded two policemen.
The interior ministry said the bomb exploded in eastern Cairo's Alf Maskan neighbourhood, where a similar blast on Friday wounded four policemen and a civilian.
Jihadist group Ajnad Misr (Soldiers of Egypt) claimed both blasts.
Two suspected militants were also killed when they mistakenly blew themselves up in an attempt to sabotage an electricity tower in the Nile Delta province of Baheira, the interior ministry said.
Tensions had surged ahead of the anniversary, and a female demonstrator was killed in clashes with police during a rare leftwing protest in Cairo on Saturday.
Shaima al-Sabbagh, who friends said was 34 and the mother of a five-year-old boy, died of birdshot wounds, a health ministry spokesman said.
Fellow protesters said she was hit by birdshot when police fired to disperse the march. Prosecutors have launched a probe into her death.
An 18-year-old female protester was also killed on Friday in clashes in Alexandria.
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Egypt has been gripped by political turmoil since Mubarak's ouster, and by violent unrest since his successor Morsi was overthrown by then army chief Sisi.
Sisi toppled Morsi in July 2013 and has since led a crackdown on his supporters that has left hundreds dead.
Jihadist militants have in turn regularly targeted security forces, killing scores of policemen and soldiers.
'FUNERAL OF THE REVOLUTION'
Ahead of the anniversary, police had warned they would "decisively" confront protests. Morsi's supporters often hold small rallies that police quickly disperse.
Cairo's streets were largely deserted, although a few Sisi supporters gathered outside Tahrir waving Egyptian flags and chanting "Long Live Egypt!"
Plainclothes police checked identity cards and stopped people from heading to the square.
Security was beefed up elsewhere in the capital, with machinegun-wielding police deployed on key streets.
"This is the funeral of the (2011) revolution," Mamdouh Hamza, a prominent figure from the anti-Mubarak uprising, told an AFP correspondent in central Cairo.
"The murderer kills, and then joins the funeral procession. Nothing has improved or changed since Sisi took over."
Activists, including those who spearheaded the anti-Mubarak revolt, have accused Sisi of reviving much of Mubarak's autocratic rule.
Sisi and his supporters deny such allegations, pointing to his widespread popularity and support in Egypt for a firm hand in dealing with protests, which are seen as threatening economic recovery.
The revolt against Mubarak erupted on January 25, 2011, with hundreds of thousands of protesters taking to the streets across Egypt for 18 days until he stepped down.
The anti-Mubarak revolt was fuelled by police abuses and the corruption of the strongman's three-decade rule, but the police have since regained popularity amid widespread yearning for stability.