Egypt's ruling military has apologised for the deaths of protesters in clashes with police, as unrest in Cairo and other cities enters its sixth day. The Supreme Council of the Armed Forces said it regretted "the deaths of martyrs from among Egypt's loyal sons". The unrest, which began on Friday, come days before the first elections since President Hosni Mubarak was ousted. At least 35 people have been killed. Protesters have rejected a pledge to speed up transition to civilian rule. They have vowed to continue their protest until the country's military rulers stand down. On Wednesday street battles continued late into the night, and were heaviest around the fortified interior ministry off Tahrir Square in Cairo. The clashes were followed by a lull. But the protesters vowed to continue occupying the square until their demands are met. "He goes, we won't," one banner read in a reference to the head of the military council, Field Marshal Mohamed Hussein Tantawi. In Alexandria protests have been smaller than in Cairo, but one protester said clashes were continuing early on Thursday outside the security headquarters. The clashes are the longest outbreak of violence since the 18-day uprising that toppled Mr Mubarak in February. The BBC's Jeremy Bowen in Cairo says the violence threatens to overshadow next week's parliamentary elections. He says public opinion on the protests is divided. Some Egyptians want elections to go ahead unhindered while others believe the military must be swept from power first. The main opposition group, the Muslim Brotherhood, is not supporting the protests and expects to do well in the elections. Rising casualties Earlier on Wednesday, UN human rights chief Navi Pillay condemned the "clearly excessive use of force" by Egypt's security forces during the clashes. She called for an independent inquiry into deaths. Groups of stone-throwing demonstrators have been locked in pitched battles in the streets between Tahrir Square and the interior ministry since the weekend. Protesters have spoken of gunshots and injuries or deaths from live bullets but Interior Minister Mansour el-Essawy said security forces were only firing tear gas. The protests have continued despite an attempt by Field Marshal Tantawi to defuse the situation by promising presidential elections by the end of June, six months sooner than planned. He also accepted the resignation of military-appointed civilian cabinet. But in his address on Tuesday, Field Marshal Tantawi offered no apologies for the violence.