The defendants faced charges over an attack on a police station in Minya in 2013 in which a policeman was killed.
However, the judge also commuted to life terms 492 death sentences out of 529 passed in March in a separate case.
Also on Monday, a court banned a youth group that helped ignite the uprising that toppled Hosni Mubarak in 2011.
The decision passed in Cairo to outlaw the April 6 pro-democracy movement was based on a complaint that accused the group of “tarnishing the image” of Egypt and colluding with foreign parties.
Ahmed Maher, the group’s leader, was sentenced to three years in prison in December for violating a law that bans all but police-sanctioned protests.
The cases and speed of the mass trial hearings have drawn widespread criticism from human rights groups and the UN.
The trials took just hours each and the court prevented defense lawyers from presenting their case, according to Human Right Watch.
The sentences have been referred to the Grand Mufti – Egypt’s top Islamic authority – for approval or rejection, a step which correspondents say is usually considered a formality. A final decision will be issued in June.
Authorities have cracked down harshly on Islamists since President Mohamed Morsi, who belongs to the Muslim Brotherhood, was removed by the military in July.
Hundreds have been killed and thousands arrested.
The verdict was the first against Mohammed Badie in the several trials he faces on various charges along with Mohamed Morsi himself and other Brotherhood leaders.
Of the 683 sentenced on Monday, only about 50 are in detention but the others have a right to a retrial if they hand themselves in.
The group was accused of involvement in the murder and attempted murder of policemen in Minya province on August 14, the day police killed hundreds of Muslim Brotherhood supporters in clashes in Cairo.
Defense lawyers boycotted the last session, branding it “farcical.”
The final judgement on the sentencing of the 529 Muslim Brotherhood supporters accused of attacking another police station in the same province on the same day means 37 will now face the death penalty.
Defense lawyer Khaled Elkomy said 60% of those defendants, including teachers and doctors, have evidence that “proves they were not present” when that station was attacked, a statement released by human rights group Avaaz said.
Last month, the UN human rights commissioner condemned the two trials and said they had breached international human rights law.
A spokesman for Navi Pillay said the “cursory mass trial” was “rife with procedural irregularities.”
The government had defended the court’s handling of the first mass case, insisting that the sentences were passed only “after careful study” and were subject to appeal.
At least 1,000 opponents of the military-installed regime have been sentenced since December. As well as the death sentences, the jail terms passed range from six months to life.
The authorities have designated the Brotherhood a terrorist group, blaming it for a series of bombings and attacks. The group has strongly denied the accusations.
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