* EU questions financial aid to Egypt since bloodshed
* Bloc still has clout as mediator
* Military aid to Egypt debated (Recasts with quotes from ministers before meeting)
By Justyna Pawlak and John O'Donnell
BRUSSELS, Aug 21 (Reuters) - The European Union was expected on Wednesday to shy away from making immediate cuts in financial aid to Egypt but several EU governments pushed for the withdrawal of military support from Europe for Cairo's army-backed rulers.
At an emergency meeting in Brussels, EU foreign ministers debated how to use their economic muscle to force the government to end a crackdown on deposed President Mohamed Mursi's Muslim Brotherhood and resume talks over a peaceful compromise.
Western governments have struggled to agree a response since the army overthrew Egypt's first freely elected leader on July 3. Calls for tougher international action grew louder in the past week after the Egyptian authorities defied Western pleas for restraint and ordered the storming of camps of Mursi supporters, in which hundreds of protesters were shot dead.
There may be little Europe can do to inflict hardship on the authorities with aid cutbacks because much of its cash goes to civil society groups, not the government, and Saudi Arabia has vowed to plug any shortfall if support is stopped.
Europe's main concern in formulating a response, several ministers said, is to ensure its role as a mediator is protected and to prevent further escalation of the conflict.
Britain's Foreign Secretary William Hague said the EU needed to "promote dialogue in Egypt".
"We have to leave the door open to doing that in the future," he told reporters ahead of the meeting in Brussels.
The EU emerged as an important mediator in diplomatic efforts which ultimately failed to prevent the storming of the Brotherhood camps.
Its foreign policy chief Catherine Ashton was the first foreign official to see Mursi since he was put in detention, reflecting the EU's image in Egypt as a neutral player, compared with Washington which is viewed with suspicion by both sides.
Dutch Foreign Minister Frans Timmermans said Europe should ensure it was in a position to facilitate talks "once the parties were prepared to talk to each other."
"All the violence we have seen has put the radical elements on both sides in the driver seat and we need more moderate people to be heard again and to be able to play a role," he said.
Diplomats said the ministers were likely to agree that any support from the EU's 5 billion euro ($6.7 billion) package of grants and loans should be kept as long as it is used to fund charities or civil society projects, as most is.
Some military aid could be withdrawn, although some governments have expressed concerns that the Cairo authorities may need some help in dealing with attacks by Islamist militants in the lawless north Sinai region, diplomats said.
Egypt's main source of military assistance is the United States, which supplies its army with $1.3 billion a year, most spent to buy and maintain U.S.-made weapons.
Britain has already suspended some joint work with the Egyptian security forces and revoked export licences. Hague has said in the past the EU could not rule out future assistance.
Underlining unease in the West over how to respond to the crisis in Egypt, the White House said on Tuesday media reports that it had cut off aid to Egypt were inaccurate although the policy was under review.
Western countries worry that abruptly cutting aid would shut dialogue with rulers of the most populous Arab country.
"It's important that we don't close off ... any channels of communication. We have an interest in Egypt not descending into complete instability. That's a European interest," Germany's foreign minister Guido Westerwelle said.
Other than aid, foreign ministers will discuss any military support provided by individual European governments to Egypt and, possibly, trade breaks included in a decade-old broad cooperation deal with Cairo. EU trade with Egypt runs at around 2 billion euros a month. ($1 = 0.7448 euros) ($1 = 0.7448 euros) (Reporting by Justyna Pawlak; Editing by Andrew Heavens and Peter Graff)