* Authorities build concrete wall to protect embassy
* Egypt's Islamist president faces tough balancing act
* Mursi condemns film, pledges to protect embassies
* Protester killed in clash with police near embassy
* United States is major aid donor to Egypt
By Edmund Blair and Tamim Elyan
CAIRO, Sept 14 (Reuters) - One protester was killed on Friday as Egyptians angry at a film denigrating the Prophet Mohammad clashed for a third day with police blocking the way to the U.S. Embassy.
The 35-year-old protestor died from bird shot wounds three days after protesters climbed embassy walls and tore down the American flag.
"God is Greatest" and "There is no God but God," one group near the front of the clashes chanted as some threw stones on Friday on a street leading from Tahrir Square to the embassy nearby, as police in riot gear fired off rounds of teargas.
Hundreds of protesters gathered in streets near the mission late into the evening, pelting police with stones and petrol bombs as they were pushed back from the embassy perimeter.
The state news agency said 27 people were injured on Friday. Based on figures it announced on other days, that suggested more than 250 people have been injured since clashes erupted on Wednesday, after Tuesday's breach of the embassy.
Elsewhere, thousands of people joined peaceful protests after Friday prayers in Tahrir and outside mosques in Cairo and other cities, responding to a call by the Muslim Brotherhood, the group that propelled President Mohamed Mursi to power.
In Sinai, militants attacked an international observer base close to the borders of Israel and Gaza, a witness and a security source said. Two Colombian soldiers were wounded, an official from the observer force said.
U.S. Defense Secretary Leon Panetta called his Egyptian counterpart, General Abdel Fattah al-Sisi, on Friday to "underscore the importance of ensuring the safety and security of the U.S. diplomatic mission," Pentagon spokesman George Little said.
"In light of ongoing protests in Egypt, Minister al-Sisi reiterated Egypt's commitment to secure U.S. diplomatic facilities and personnel," Little said.
Many Muslims regard any depiction of the Prophet Mohammad as blasphemous and the low-budget film - produced in California - that portrayed him as a womanizer and religious fake has provoked outrage across the Middle East and led to the storming of several U.S. missions in the region.
Mursi, an Islamist and Egypt's first freely elected leader, has to strike a delicate balance, fulfilling a pledge to protect the embassy of a major aid donor but also delivering a robust line against the film to satisfy his Islamist backers.
Mursi repeated on Friday his condemnation of the film, rejection of violence and promise to protect diplomatic missions in comments in Italy, the second stop of a trip to Europe.
On Thursday, he said he asked U.S. President Barack Obama to act against those seeking to harm relations. His cabinet said Washington was not to blame for the film but urged the United States to take legal action against those insulting religion.
Obama's administration says it had nothing to do with the film but cannot curb the constitutional right to free speech in the United States.
U.S. AID
Washington has a large embassy in Cairo, partly because of a vast aid program that began after Egypt signed a peace deal with Israel in 1979. Washington gives $1.3 billion in aid each year to Egypt's army plus additional funds for its government.
Washington, a close ally of Egypt under deposed president Hosni Mubarak, has long been wary of Islamists, only formally opening contacts with the Brotherhood last year, several months after he was forced from power by a popular uprising.
Al-Masry Al-Youm highlighted comments Obama made to a Spanish-language network saying Egypt was neither an enemy nor an ally, underlining the changing ties. "America: Egypt is no longer an ally," the newspaper wrote in a front-page headline.
"Before the police, we were attacked by Obama, and his government, and the Coptic Christians living abroad!" shouted one protester wearing a robe and long beard favoured by some ultra-orthodox Muslims, speaking close to the police cordon.
Egypt's Coptic Orthodox church has condemned what it said were Copts abroad who had financed the film. Many Copts worry about the rise of Islamists and fret about any action that could stoke tensions between the two communities.
Two Islamist preachers in Egypt told worshippers on Friday those who made the film deserved to die under sharia, Islamic law, but said diplomats and police should not be targeted.
Although this could be taken by some Muslims as an edict to take the law into their hands, many Egyptians believe only the prestigious Al-Azhar mosque has the authority to issue decrees.
An Al-Azhar preacher said protests should be peaceful. The state news agency said a team of Al-Azhar officials urged those battling with police to stop.
One banner held aloft by demonstrators read: "It is the duty of all Muslims and Christians to kill Morris Sadek and Sam Bacile and everyone who participated in the film."
The two people named were both linked to the film. Sadek, a Copt living in the United States, told Reuters this week he promoted the film to highlight discrimination against Christians who make up about 10 percent of Egypt's 83 million people.
The violence has angered many Egyptians. One image circulating on Facebook showed a charred car accompanied by the words: "People go to defend the Prophet with petrol bombs and religious insults to the police. They don't pray at noon or in the afternoon. Who are they?"
Though some demonstrators clashing with police near the embassy wore clothes favoured by ultra-orthodox Islamists, most were young men or youths in jeans and T-shirts. Some made it clear they did not back Mursi or have Islamist sentiments.
"Mursi is protecting them and attacking us, he should allow us in," said Mohamed Mustafa, 20, a ceramics worker who voted for a liberal rival of Mursi's in the presidential election.
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