* Petrol bombs thrown at presidential palace - witnesses
* At least 59 killed in wave of unrest since Jan. 25 (Adds cabinet statement, new number of wounded)
By Alexander Dziadosz
CAIRO, Feb 8 (Reuters) - Egyptians marched and chanted against Islamist President Mohamed Mursi in cities across the country on Friday and several hundred attacked the presidential palace with petrol bombs and rocks.
At least 126 people were hurt in unrest in various provinces, state media said, while two officers and three soldiers of the Republican Guard were wounded in clashes.
Protests erupted last month over what demonstrators saw as Mursi's attempts to monopolise power as well as wider political and economic grievances.
The main opposition alliance signed an agreement with the ruling Muslim Brotherhood last week rejecting violence and had not officially called for marches on Friday, although some of the alliance's younger members called for protests.
While the number of protesters has dwindled, distrust of Mursi and the Brotherhood and a sense of political and economic malaise have continued to bring people into the streets.
At least 59 people were killed in the demonstrations between Jan. 25, second anniversary of the uprising that toppled President Hosni Mubarak two years ago, and Feb. 4.
A few hundred protesters gathered outside the presidential palace in Cairo as night fell, throwing stones and homemade bombs at the main gate. Police fired into the air, shot teargas and drove cars toward the crowd to scatter them.
"The people want to overthrow the regime," the protesters chanted, turning the slogan of Arab Spring protests against the Islamist-led government they helped bring to power.
In Zagazig north of Cairo, protesters gathered in the area of Mursi's home, MENA said. The demonstrators threw rocks at police, who fired teargas back.
Egypt's Prime Minister Hisham Kandil condemned the unrest and said the protests' organisers had to prevent the violence and stop "criminal elements" from carrying out destruction.
"Violence cannot be justified under any name. It is reprehensible behaviour that harms the stability of the country and obstructs the interests of its citizens," he said in a statement.
Two years after sweeping autocratic rulers from power, many in Egypt and Tunisia are angry over what they see as an attempt by Islamists to hijack their revolutions without improving their prospects for a better life.
In Tunisia, police and mourners clashed at the mass funeral of secular opposition leader Chokri Belaid, whose assassination on Wednesday plunged the country deeper into political crisis.
Some of the most violent clashes on Friday were in the Nile Delta town of Tanta, hometown of an activist, 23-year-old Mohamed el-Gendi, who was buried there this week after being beaten to death by security men in Cairo.
Television footage showed scores of protesters lobbing petrol bombs at riot police, who responded with teargas to scatter the demonstrators.
"Down, down with the rule of the Supreme Guide," protesters chanted, referring to Mohamed Badie, leader of the Brotherhood, which has dominated Egypt's politics since the fall of Mubarak.
In al-Mahalla al-Kubra, another delta town, protesters threw bombs and broke down the door of a city council building as they tried to break in, MENA reported. Police fired teargas to disperse them.
The Brotherhood's Freedom and Justice Party issued a statement on its Facebook page condemning "the attempts of some political forces in al-Mahalla al-Kubra to incite violence and destruction of public property".
In Kafr el-Sheikh, dozens of protesters pelted police with rocks and tried to storm a government building to demand the removal of the provincial governor, MENA said.
At a subway station near Tahrir Square, epicentre of the 18-day revolt that toppled Mubarak, demonstrators stopped trains by climbing onto the tracks, MENA reported.
In the town of El-Santa in Gharbiya province, protesters threw rocks at the offices of the Freedom and Justice Party, the Brotherhood's political party, MENA reported. (Reporting by Alexander Dziadosz; Additional reporting by Omar Fahmy; Editing by Paul Taylor, Angus MacSwan and Roger Atwood)