* Cairo wants Egyptian-born Qaradawi extradited
* Egypt's ties to Qatar strained since military takeover
* Four foreigners face trial for aiding "terror group" (Adds Qatari comment)
By Maggie Fick
CAIRO, Feb 4 (Reuters) - Egypt's Foreign Ministry said on Tuesday it had summoned Qatar's chargé 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 had been 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 that recent comments by Qaradawi, who said Saudi support for the military government was wrong and should be withdrawn, were unacceptable and criticised the wealthy Gulf Arab state for its "refusal to hand over wanted Egyptians".
Qaradawi is among 130 people including ousted Islamist president Mohamed Mursi who have been sent to trial in connection with a mass jailbreak during the 2011 uprising that ousted Hosni Mubarak.
Qatar had given heavy diplomatic and financial backing to Mursi during his year in power, but ties have soured since he was ousted by the army last July following mass protests against his rule.
Since then, Egypt has pursued a wide crackdown against Mursi's Muslim Brotherhood and designated it a terrorist group. Some members of the Brotherhood and other opponents of the government fled to Qatar.
The foreign ministry summoned Qatar's ambassador last month after Doha criticised the crackdown.
Egypt accuses Qatar and its television channel Al Jazeera of backing the Muslim Brotherhood.
Qatari Foreign Minister Khaled al-Attiyah said in a television interview this week that Qatar had supported successive Egyptian governments. "We don't support a party or a faction - our position is clear," he said.
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 organisation".
He referred to the foreigners as Al Jazeera correspondents, but the network told Reuters that it did 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 Dec. 29 and remain in custody.
The network described the charges as absurd.
Most of the 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 Mursi.
Their hereditary rulers were close allies of Mubarak, and saw the rise 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 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 in recent days over what it called insults against the UAE made by Qaradawi in a broadcast from Doha. (Additional reporting by Amena Bakr in Doha; Writing by Maggie Fick; Editing by Michael Georgy and Tom Heneghan)