* Cairo wants Egyptian-born Qaradawi extradited
* Egypt's ties to Qatar strained after military takeover
* Four foreigners face trial for aiding "terror group"
By Maggie Fick
CAIRO, Feb 4 (Reuters) - Egypt's foreign ministry said on Tuesday it had summoned Qatar's charge d'affaires to demand the extradition of Youssef al-Qaradawi, one of the most influential Sunni Muslim clerics in the Middle East.
Ministry spokesman Badr Abdelatty said the diplomat was told Egypt wanted Qatar to extradite critics of Cairo's army-backed government, including the Egyptian-born cleric who supports the now-banned Muslim Brotherhood.
Abdelatty told journalists recent comments by Qatar-based Qaradawi, who said Saudi support for the military government was wrong and should be withdrawn, were unacceptable and criticized Doha for its "refusal to handover wanted Egyptians."
Qaradawi faces charges alongside ousted Islamist President Mohamed Mursi in connection with a mass jail break during the 2011 uprising that ousted Hosni Mubarak.
Once close Qatari-Egyptian ties have soured since Cairo's army last July ousted Mursi, who was strongly backed by Doha, following mass protests against his one-year rule.
Egypt then launched a wide crackdown against Mursi's Muslim Brotherhood group and labeled it a terrorist group. Some members of the Brotherhood and other opponents of the government fled to Qatar, a wealthy Gulf Arab state.
The foreign ministry summoned Qatar's ambassador last month after Doha criticized Cairo's crackdown on the Muslim Brotherhood.
Egypt accuses Qatar and its Doha-based Al Jazeera television channel of backing the Muslim Brotherhood.
FOREIGNERS FACE TRIAL
Egypt's public prosecutor said last week that he would put an Australian, two Britons, and a Dutchwoman on trial for aiding 16 Egyptians belonging to a "terrorist organization."
He referred to the foreigners as Al Jazeera correspondents, but the Qatar-based television network told Reuters that it does not have any Dutch or British correspondents in Egypt.
Three Al Jazeera journalists - Australian Peter Greste, Canadian-Egyptian Mohamed Fahmy and Egyptian Baher Mohamed - were detained in Cairo on December 29 and remain in custody.
The network described the charges as absurd.
Most U.S.-aligned Gulf Arab monarchies, rattled by the rise of Islamists in the Middle East, were relieved when the Egyptian military stepped in to topple President Mohamed Mursi after mass protests against his rule.
The hereditary rulers of most Gulf Arab states were close allies of Mubarak, and they saw the subsequent rise to power of the Brotherhood in Egypt as a dangerous precedent that could embolden Islamists at home.
Saudi Arabia, the United Arab Emirates and Kuwait have pumped billions of dollars into Egypt since the army takeover to help the government keep the economy afloat.
During Mursi's year in office, Qatar lent or gave Egypt $7.5 billion.
The United Arab Emirates summoned the Qatari ambassador over what it called insults against the UAE made by Qaradawi in a broadcast from Doha, state news agency WAM reported on Sunday.
(Additional reporting by Amena Bakr in Doha; Writing by Maggie Fick; Editing by Michael Georgy and Tom Heneghan)