* Lawyers say they can't hear Mursi in court cage
* Mursi on trial in three cases, charged in two others
* Muslim Brotherhood accused of plotting with Hamas, Iran (Re-leads with withdrawal of Mursi's lawyers from proceedings)
By Michael Georgy
CAIRO, Feb 16 (Reuters) - Lawyers for deposed Egyptian President Mohamed Mursi withdrew in protest after he appeared in court on Sunday on charges of conspiring with foreign groups to commit terrorist acts in Egypt.
Mursi's legal team protested they could not hear their client speak from inside a soundproof glass cage. The judge controls the microphone that allows defendants to be heard.
The judge ordered a lawyer's syndicate to assign 10 lawyers to defend Mursi at the trial's next hearing on Feb. 23.
"My professional conscience will not permit me to continue...in these void proceedings," lawyer Mohamed Salim al-Awa told Reuters.
In what they call "the biggest case of conspiracy in the history of Egypt", prosecutors say Mursi's Muslim Brotherhood hatched a "terrorist plan" in 2005 involving the Palestinian Hamas group as well as Shi'ite Iran and its Lebanese ally Hezbollah.
Hamas has dismissed the charges as "fabrications and lies". The Brotherhood also rejects the allegations, saying it is a peaceful organisation with no links to any violent groups.
The Brotherhood accuses the army of staging a coup and reviving a dictatorship, an allegation the military denies.
Islamic militant groups have stepped up bombing and shooting attacks on security forces since Mursi's fall, killing hundreds.
In the latest attack in Sinai, an explosion on a tourist bus killed two Koreans and the Egyptian driver on Sunday, security sources said.
The Brotherhood propelled Mursi to election victory in 2012 but was driven underground after the army ousted the Islamist leader in July after mass protests against his rule.
The state, which has declared the Brotherhood a terrorist group, has killed about 1,000 of its members on the streets and jailed thousands, including its top leaders.
Egypt's Western allies have exerted little pressure on Cairo to end what critics say are widespread human rights violations.
Mursi is on trial in three cases and charged in two others.
In the latest case, the prosecutor also charged Brotherhood leaders Mohamed Badie, Khairat El-Shater, Mahmoud Ezzat and others with crimes including committing acts of terrorism in Egypt and divulging military secrets to a foreign state.
A total of 36 people are on trial.
"What are you so afraid of? Are you afraid because you have no public support?" Mursi asked the panel of judges.
The prosecution has said the Brotherhood's plan was to send "elements" to the Hamas-controlled Gaza Strip for military training by Hezbollah and the Iranian Revolutionary Guards.
Upon their return to Egypt, they would join forces with militant groups in the Sinai Peninsula, the Egyptian territory that borders Israel to the east, it has alleged.
After the 2011 uprising that ousted President Hosni Mubarak, the Brotherhood exploited the chaos to carry out attacks on security forces in North Sinai and elsewhere, it said.
The prosecutor said the plotters aimed to establish an "Islamic emirate" in North Sinai if Mursi had not been declared president after the 2012 presidential election.
He said Mursi's presidential aides, including Essam El-Haddad, his national security adviser, had leaked secret reports to Iran's Revolutionary Guards and Hezbollah as a reward for their cooperation in the conspiracy.
After crushing the Brotherhood at home, Egypt's military rulers plan to undermine Hamas, senior Egyptian security officials and diplomats have told Reuters.
The aim, which the officials said could take years to pull off, includes working with Hamas's political rivals Fatah and supporting popular anti-Hamas activities in Gaza. (Additional reporting by Yasmine Saleh and Maggie Fick; Editing by Alistair Lyon)