* Largest mass death sentence in modern history - lawyers
* Brotherhood demands army downfall, relatives decry verdict
* State media report ruling, no immediate response from govt
* U.S. voices shock at sentences (Adds U.S. State Department reaction, paragraphs 4, 10-11)
By Asma Alsharif
CAIRO, March 24 (Reuters) - An Egyptian court sentenced 529 members of the outlawed Muslim Brotherhood to death for murder and other offenses on Monday in a sharp escalation of a crackdown on the movement that is likely to fuel instability.
Family members stood outside the courthouse screaming after the verdict, which defense lawyers called the biggest mass death sentence handed out in Egypt's modern history.
Turmoil has deepened since the army overthrew Egypt's first freely elected president, Mohamed Mursi of the Muslim Brotherhood, in July. Security forces have killed hundreds of Brotherhood members in the streets and arrested thousands.
Human rights groups said Monday's verdict suggested the authorities intended to tighten their squeeze on the opposition. The U.S. State Department said it was shocked by the death sentences.
State television reported the sentences without comment. A government spokesman did not immediately respond to calls and several government officials said they could not comment on judicial matters.
"The court has decided to sentence to death 529 defendants, and 16 were acquitted," defense lawyer Ahmed al-Sharif told Reuters. The condemned men can appeal against the ruling.
Most of the defendants at Monday's hearing were detained and charged with carrying out attacks during clashes that erupted in the southern province of Minya after the forced dispersal of two Muslim Brotherhood protest camps in Cairo on Aug. 14.
"We did not expect such a brutal sentence. But at the same time this military regime just wants to kill anybody who wants to express an opinion," Sayaf Gamal, one of the Brotherhood members sentenced to death, said by telephone. He is on the run.
"They are willing to kill everybody so that there is no freedom of expression," Gamal said.
"We're certainly raising it with the Egyptian government ... it's a pretty shocking number," State Department spokeswoman Marie Harf said of the sentences. "It defies logic that over 529 defendants could be tried in a two-day period in accordance with international standards."
Harf added that the United States still considered its ties with Egypt to be important and added: "We don't want to completely cut off the relationship."
'THE QUICKEST CASE'
Islamist militants have stepped up assaults on the police and army since Mursi's ouster, killing hundreds and carrying out high-profile operations against senior Interior Ministry officials.
The Muslim Brotherhood, which has been largely driven underground, responded to the death sentences by calling for the "downfall of military rule" on its official website.
Mohamed Mahsoub, who served as minister of legal affairs under Mursi, used his Facebook page to describe the court's decision as "a ruling calling for the execution of justice".
Supporters set fire to a nearby school in protest, state television reported, although security officials said they had received no reports of unrest.
The charges against the group on trial in Minya since Saturday include violence, inciting murder, storming a police station, attacking persons and damaging public and private property.
"This is the quickest case and the number sentenced to death is the largest in the history of the judiciary," said lawyer Nabil Abdel Salam, who defends some Brotherhood leaders including Mursi.
"A second year student in the faculty of law would never issue this verdict. There are a lot of flaws in this verdict. I think maybe an appeal could be successful but nothing is predictable," said Mohamed Zaree, program manager for the Cairo Institute for Human Rights Studies.
H.A. Hellyer, an Egypt expert and fellow at the Brookings Institution U.S. think tank, said he doubted the sentences would be carried out. "Nevertheless, the very issuing of the sentence itself is quite significant," he added.
On Tuesday, Muslim Brotherhood Supreme Guide Mohamed Badie and 682 others will face trial on charges of incitement to kill.
Only 123 of the defendants were in court. The rest were either released, out on bail or in hiding.
"When the trial starts on Saturday and it is just a procedural hearing, and the judge doesn't listen to any lawyers or witnesses and doesn't even call the defendants, you are before a group of thugs and not the judiciary," Walid, a relative of one of the defendants, said by phone.
It was not possible to confirm his account of the proceedings independently.
The government has declared the Brotherhood a "terrorist" group, but the group says it is committed to peaceful activism.
Analysts say some of its members could turn violent if the state keeps up pressure on the movement, which won the vast majority of elections since a popular uprising toppled autocrat Hosni Mubarak in 2011.
Egyptian authorities make no distinction between the Brotherhood and hardcore militant groups based in the Sinai peninsula that pose a major security challenge to the state despite army offensives against their fighters.
Mursi, Mubarak's successor as president, and other top Brotherhood leaders are on trial on a range of charges and accuse the military of staging a coup and undermining democracy.
The army says it was acting on behalf of the Egyptian people, who took to the streets in their millions to call for Mursi's resignation. (Additional reporting by David Brunnstrom in Washington; Writing by Michael Georgy; Editing by Tom Heneghan, Peter Cooney and Tom Brown)