* Foreign minister blames Brotherhood, urges dialogue
* Human rights body denounces police violence
* Two killed in clashes in Suez Canal city
* EU's Ashton to meet army chief in Cairo (Updates with Ashton quote, Port Said violence)
By Maggie Fick and Yasmine Saleh
CAIRO, July 28 (Reuters) - Thousands of Muslim Brotherhood supporters stood their ground near a Cairo mosque on Sunday, a day after at least 72 were shot dead by Egyptian security forces, braced for a move against them by the army chief who ousted Islamist President Mohamed Mursi.
General Abdel Fattah al-Sisi made his first appearance since Saturday's bloodshed, smiling before television cameras at a graduation ceremony for police recruits in starched white uniforms.
He received a standing ovation and was hailed by Interior Minister Mohamed Ibrahim as "Egypt's devoted son". Fawning coverage in state and private media reflected Sisi's rising political star, in a country ruled by former military officers for six decades before Mursi's election in 2012.
Saturday's dawn killings, following a day of rival mass rallies, fuelled global anxiety that the most populous and influential Arab nation risked broader conflagration.
The European Union said it was sending foreign policy chief Catherine Ashton to meet on Monday with Sisi and the interim president he installed, as well as officials of the Freedom and Justice Party, the Brotherhood's political wing.
Ashton said she would press for a "fully inclusive transition process, taking in all political groups, including the Muslim Brotherhood".
The Brotherhood accuses the military of reversing the 2011 uprising that toppled Hosni Mubarak, and demands that Mursi, Egypt's first freely elected president, be reinstated.
Mursi has been in army detention since his July 3 overthrow and the military-backed interim government has placed him under investigation on charges including murder. Authorities also say they will move soon to clear the Brotherhood's tent vigil.
"It's a source of terrorism that's threatening the whole society, and that's being confirmed by the day," Mostafa Hegazy, adviser to interim President Adli Mansour, told reporters.
Army vehicles surrounded entrances to the square outside the Rabaa al-Adawiya mosque in northern Cairo, where Brotherhood supporters used pictures of the bearded Mursi to shelter from the fierce sun.
"We are right, legitimacy is on our side and hopefully at the end God will lead us to triumph and we will not give up," said Mostafa Ali, 29, from the Nile delta town of Mansoura.
The Interior Ministry has rejected witness accounts that police fired on the crowds and a public prosecutor has launched a probe into the violence, investigating 72 suspects for an array of crimes including murder and blocking streets.
Cairo was quiet on Sunday, but violent clashes rattled the Suez Canal city of Port Said, where security sources said two people were killed, including a 17-year-old, in fighting between pro- and anti-Mursi camps. Twenty-nine people were wounded.
The violence has polarised Egypt, with its secular and liberal elite showing little sympathy for the Brotherhood or qualms about the military's return to the political frontline.
Speaking to Reuters, interim Foreign Minister Nabil Fahmy said deepening divisions would lead to "more tragedies". He blamed the Brotherhood for the violence, but said they should be part of the country's political future.
"If they decide to withdraw from politics, it will be disappointing, if they decide to pursue violence, then you are looking at a completely different confrontation," Fahmy said. "Even if I personally reject their positions or ideology, they have to find their place in Egypt's political life."
In a first sign of doubt from within the interim cabinet installed after the military takeover, Deputy Prime Minister for Economic Affairs Ziad Bahaa El-Din said the government must not copy the "oppressive" policies of its foes. "Excessive force is not permitted," Bahaa El-Din wrote on Facebook.
The Tamarud youth protest movement, which mobilised millions of people against Mursi and has fully backed the army, expressed alarm at an announcement by Interior Minister Ibrahim that he was reviving Mubarak's hated secret political police, shut down after his fall.
"CAN'T REWRITE HISTORY"
The military says it does not want to retain power and aims to hand over to full civilian rule with a "road map" to parliamentary elections in about six months. But the very public role of Sisi as face of the new order has sown doubt.
New York-based Human Rights Watch said the Saturday killings suggested a "shocking willingness" by police and politicians to ratchet up violence against backers of Mursi. U.N. human rights chief Navi Pillay said confrontation was "leading to disaster".
"Egypt stands at a crossroads," Pillay said in a statement. "The future of this great country that gave so much to civilization depends on how its citizens and authorities act over the following days and months."
Nearly 300 people have died in violence since Sisi deposed Mursi. The National Defence Council - comprising the interim president and heads of the security forces - said it was committed to freedom of expression and protest, providing they were peaceful. It urged Mursi supporters to "stop practicing violence and terrorism".
Besides the Cairo bloodshed, some of the worst violence has been in the lawless Sinai peninsula, which borders Israel and the Palestinian Gaza Strip, where Islamist militants have attacked security forces almost daily.
State news agency MENA said on Sunday that 10 "terrorist elements" in north Sinai had been killed and 20 arrested in security sweeps over the past 48 hours.
Islamist politician and former presidential candidate Mohamed Selim al-Awa offered a compromise that would see Mursi reinstated but with new elections within months. It was rejected by the interim presidency and Egypt's biggest liberal and leftist coalition, the National Salvation Front (NSF).
"It's clearly a non-starter," said NSF spokesman Khaled Dawoud. "You can't rewrite history; Mursi is out and there is already a road map."
(Additional reporting by Shadia Nasralla, Yasmine Saleh, Tom Finn, Omar Fahmy, Michael Georgy, Noah Browning, Tom Perry and Asma Alsharif, Patrick Werr in Cairo, Yusri Mohamed in Ismailia; Writing by Crispian Balmer and Matt Robinson; Editing by Michael Georgy and Giles Elgood)