* Brotherhood HQ and office in suburbs set on fire
* Officials blame police for failing to prevent violence
* President wants national dialogue, protesters refuse
CAIRO, Dec 6 (Reuters) - The Muslim Brotherhood's main office in the Egyptian capital and an office used by the Islamist group in a suburb south of Cairo were set on fire late on Thursday, Brotherhood officials and state media said.
Egypt has been in turmoil since President Mohamed Mursi issued a decree on Nov. 22 awarding himself wide powers. On Wednesday night, seven people were killed in clashes around the presidential palace before security forces stopped the fighting.
The Brotherhood's Freedom and Justice Party (FJP) said on its Facebook page that the headquarters in the Mukattam district had been attacked in "a terrorist aggression" by thugs.
The state news agency said the office used by the FJP was set ablaze in the suburb of Maadi. Another office was broken into near the city centre, it said.
Brotherhood officials blamed police for failing to prevent the violence. "There was an intensive presence of security forces in front of the Brotherhood's main headquarters in Mukattam, yet no one intervened to stop the protesters from burning it down," FJP's Facebook page quoted the Brotherhood's spokesman Mahmoud Ghozlan as saying.
Mursi invited in a live televised address, political groups, judges and others to meet on Saturday for a national dialogue but demonstrators and activists refused.