* Mass trials, death sentences could trigger more violence
* Brotherhood believed to have about 1 million members
* United States, EU condemn Monday's mass death sentence (Adds protests, Justice Ministry reaction, details)
By Treza Kamal
MINYA, Egypt, March 25 (Reuters) - The leader of Egypt's outlawed Muslim Brotherhood and 682 others went on trial on Tuesday on charges including murder, their lawyer said, a day after more than 500 supporters of deposed Islamist president Mohamed Mursi were sentenced to death.
Brotherhood Supreme Guide Mohamed Badie, 70, and the others were being tried in the same court in Minya Province that condemned 529 members of the Islamist group to death, in what rights groups said was the biggest mass death sentence handed out in Egypt's modern history.
Protests erupted after Tuesday's trial began, with police firing teargas to deter hundreds of demonstrators.
The U.N. human rights office said the mass death sentences contravened international law. The European Union and the United States also criticised the ruling, as did rights groups.
"Yesterday was ... a death sentence for the credibility and independence of Egypt's criminal justice system," said Nicholas Piachaud, a campaigner at Amnesty International.
"There is little hope of the 683 people indicted in this latest trial of receiving fair proceedings before the same judge who yesterday handed down death sentences so readily."
Justice Ministry official Abdel Atheem al-Ashari defended the death sentences, saying in a statement in response to the ruling that the separation between the state and the judiciary is one of the main principles of any democratic system.
There are no signs that Western powers will back their dismay with action to push for greater democracy in Egypt, which is of strategic importance because of its peace treaty with Israel and contains the Suez Canal, a global shipping lane.
Egypt has cracked down hard on the Brotherhood since army chief Field Marshal Abdel Fattah al-Sisi toppled Mursi, Egypt's first freely elected president, in July, and installed a government.
In August, security forces killed hundreds of Brotherhood supporters who staged a long sit-in to demand Mursi's reinstatement. Thousands of others were arrested and top leaders, including Mursi himself, are also on trial.
Defence lawyers boycotted Tuesday's court session - attended by 60 of the defendants - after complaining of irregularities. Reporters were barred from the courtroom.
"We refrained from attending ... because the judge has violated criminal law procedures and did not allow the (lawyers) to present their defence," Adel Ali, a member of the defence team, told Reuters.
He said those in the dock did not have an opportunity to defend themselves after their lawyers quit the proceedings.
Seventy-seven of the defendants were in custody while the rest had been released on bail or were on the run, he said. The verdicts are due on April 28.
All the charges related to clashes in Minya, a bastion of Islamist support south of Cairo, that broke out after the security forces crushed the pro-Mursi camps in the capital. A policeman was killed during the protests.
The mass trials will ratchet up tensions and could trigger more violence in the biggest Arab state, which has been dogged by political upheaval since a popular uprising backed by the army toppled veteran leader Hosni Mubarak in 2011.
Hours after Tuesday's trial began, protests broke out at Minya University. Police lobbed teargas canisters and fired in the air in an attempt to disperse hundreds of demonstrators.
In Egypt's second city Alexandria, a Reuters witness said protesters who chanted against Sisi marched out of the main gate of a university and blocked a busy road. Some raised their hands to display the four-finger sign that has become a symbol of sympathy for the Brotherhood.
Security forces fired teargas, birdshot and live bullets in the air, while protesters threw stones.
"We're coming out (to protest) today because the judiciary has become a tool in the hands of the military and the authorities," said Mohamed Ashraf, student in the faculty of commerce. "This is evidence of a military coup in Egypt."
An Islamist alliance which includes the Brotherhood has urged Egyptians to take to the streets in politically sensitive areas of Cairo to protest against the mass trials, despite severe restrictions having been imposed on demonstrations.
The sites include the Rabaa al-Adawiya mosque, scene of one of two pro-Mursi protest camps and Tahrir Square, the symbolic heart of the revolt against Mubarak.
The Brotherhood, believed to number about 1 million in a population of 85 million and which has won most elections since Mubarak was ousted, has been declared a terrorist group by the government. It says it is committed to peaceful activism.
The government has blamed it and other Islamist groups for attacks on police and soldiers since Mursi was deposed.
Hundreds have been killed and the insurgency is spreading across the country, with shootings, suicide bombings and assassinations of senior Interior Ministry officials. (Additional reporting by Asma Alsharif and Yasmine Saleh; Writing by Michael Georgy; Editing by Alison Williams)