CAIRO — Protesters denouncing Egypt’s Islamist president hurled stones and firebombs through the gates of his palace on Friday, clashing with security forces who fired tear gas and water cannons as more than a week of political violence came to Mohammed Morsi’s symbolic doorstep for the first time.

The march on the palace in an upscale district of the capital was part of a wave of demonstrations in cities around the country called by opposition politicians, trying to wrest concessions from Morsi after around 60 people were killed in protests, clashes and riots.

But many of the protesters go further, saying he must be removed from office, accusing his Muslim Brotherhood of monopolizing power and failing to deal with the country’s mounting woes. Many have been further angered by Morsi’s praise of the security forces after the high death toll, which is widely blamed on excessive use of force by the police.

The day’s unrest, however, risked boosting attempts by the government and Brotherhood to taint the opposition as violent and destructive — a tack Morsi supporters have taken for weeks.

In a statement issued amid the clashes, Morsi said “political forces involved in incitement” are responsible for the violence and spoke of an investigation. He called on all factions to condemn what he called an attempt to break into the palace and said security forces would “act decisively to protect state institutions.”

A day earlier, the top opposition figures met with the Brotherhood for the first time and agreed on a joint promise to avoid violence. That drew sharp criticism from many anti-Morsi activists who said the politicians had played into the Brotherhood’s hands and given legitimacy to any crackdown.

The streets outside the presidential palace — where Morsi was not present — were a scene of mayhem after nightfall. Police fired dozens of volleys of tear gas at a time, pushing the crowds away from the palace gates.