* Clashes across Egypt claim dozens of lives
* At least 29 protesters killed in Cairo, most shot dead
* Authorities blame Islamists for provoking violence
* Political, security crisis has divided society (updates death toll, adds foreign reaction)
By Yasmine Saleh and Tom Finn
CAIRO, Aug 14 (Reuters) - Egyptian security forces killed at least 29 people on Wednesday when they moved in to clear a camp of protesters demanding the reinstatement of deposed President Mohamed Mursi, in a dramatic dawn swoop aimed at ending a six-week standoff in Cairo.
Troops opened fire on demonstrators in clashes that brought chaos to areas of the capital and looked certain to further polarise Egypt's 84 million people between those who backed Mursi and the millions who opposed his brief rule.
In the streets around the Rabaa al-Adawiya mosque in northeast Cairo, where thousands of Mursi supporters have staged a sit-in, riot police wearing gas masks crouched behind armoured vehicles, tear gas hung in the air and burning tyres sent plumes of black smoke into the sky.
The unrest spread beyond the capital, with the Nile Delta cities of Minya and Assiut, and Alexandria on the northern coast, also hit by violence. Nine people were killed in the province of Fayoum south of Cairo. Five more died in Suez.
Seven hours after the initial operation, crowds of protesters were still blocking roads, chanting and waving flags as security forces sought to prevent them from regrouping.
At a morgue near the mosque, a Reuters reporter counted 29 bodies, including that of a 12-year-old boy. Most had died of gunshot wounds to the head.
"At 7 a.m. they came. Helicopters from the top and bulldozers from below. They smashed through our walls. Police and soldiers, they fired tear gas at children," said teacher Saleh Abdulaziz, 39, clutching a bleeding wound on his head.
"They continued to fire at protesters even when we begged them to stop."
The West, notably the United States which gives the Egyptian military $1.3 billion each year, has been alarmed by the recent violence, and on Wednesday the European Union urged security forces to show "utmost restraint" in a nation that has a peace treaty with Israel and controls the vital Suez Canal waterway.
MILITARY TIGHTENS GRIP
The move to break up the camps appeared to dash any remaining hopes of bringing the Brotherhood back into the political mainstream, and underlined the impression many Egyptians share that the military is tightening its grip.
The operation also suggested the army had lost patience with persistent protests that were crippling parts of the capital and slowing the political process.
It began just after dawn with helicopters hovering over the camps. Gunfire rang out as protesters, among them women and children, fled Rabaa, and smoke rose into the air. Armoured vehicles moved in beside bulldozers which began clearing tents.
"Tear gas (canisters) were falling from the sky like rain. There are no ambulances inside. They closed every entrance," said protester Khaled Ahmed, 20, a university student wearing a hard hat with tears streaming down his face.
"There are women and children in there. God help them. This is a siege, a military attack on a civilian protest camp."
A second, smaller camp near Cairo University was swiftly cleared in the early morning.
The government issued a statement saying security forces had showed the "utmost degree of self-restraint", reflected in low casualties compared to the number of people "and the volume of weapons and violence directed against the security forces".
It added that it would press ahead with implementing an army-backed political transition plan in "a way that strives not to exclude any party from participation".
The government, which envisages holding new elections in about six months to return democratic rule to Egypt, urged the protesters not to resist the authorities, adding that Muslim Brotherhood leaders must stop inciting violence.
"The government holds these leaders fully responsible for any spilt blood, and for all the rioting and violence going on," the statement added.
CONDEMNATION, RISING CONCERN OVERSEAS
Security officials said senior Muslim Brotherhood politician Mohamed El-Beltagi had been arrested during Wednesday's crackdown. A grouping of the movement's allies denied the assertion, but said Beltagi's daughter had been shot dead.
The Interior Ministry issued a statement saying Brotherhood leaders had instructed their followers to attack police stations throughout the country.
Live television footage on several channels appeared to show hooded Brotherhood gunmen brandishing what appeared to be small automatic rifles and firing them in the direction of soldiers.
The latest crackdown came after international efforts failed to mediate an end to the political standoff between Mursi's supporters and the army-backed government which took power after his ouster on July 3.
Iran condemned Wednesday's violence and said it increased the likelihood of civil war in Egypt.
Turkey's Prime Minister Tayyip Erdogan called on the U.N. Security Council and Arab League to take immediate steps to stop a "massacre" in Egypt, and the European Union said reports of protesters being killed were "extremely worrying".
Mursi became Egypt's first freely elected leader in June 2012, but failed to tackle deep economic malaise and worried many Egyptians with apparent efforts to tighten Islamist rule.
Liberals and young Egyptians staged huge rallies demanding that he resign, and the army said it removed him in response to the will of the people.
More than 300 people have already died in political violence since Mursi's overthrow, including dozens of supporters killed by security forces in two separate earlier incidents in Cairo.
The unrest has extended political and economic turmoil since a 2011 uprising that ended 30 years of autocratic rule by U.S.-backed President Hosni Mubarak, and the country is now more deeply divided than any time for many years. (additional reporting by Michael Georgy, Tom Perry, Shadia Nasralla, Omar Fahmy and Ashraf Fahim in Cairo and Adrian Croft in Brussels; Writing by Mike Collett-White)