* Clashes show Egypt still dangerously polarised
* Religious authority tries to convene talks
* No police move yet against pro-Mursi protesters (Re-leads with shootings)
By Tom Finn and Tom Perry
CAIRO, Aug 13 (Reuters) - The Muslim Brotherhood said on Tuesday that Egyptian policemen dressed in plain clothes opened fire on one of its marches in Cairo, wounding five people in violence that risks worsening political turmoil.
A security source said seven protesters had been wounded but added that it was not immediately clear who had opened fire.
The shooting could further inflame political divisions as the Brotherhood stages protests, marches and sit-ins to demand the reinstatement of deposed Islamist President Mohamed Mursi.
Supporters and opponents of Mursi earlier battled in the streets of the capital, showing Egypt remained dangerously split six weeks after the army overthrew him in response to mass protests against his rule.
Aside from the violence, an initiative by Al-Azhar, a top religious authority, to resolve the crisis appeared to inch forward.
The Nour Party, the second biggest Islamist group, forecast that Al-Azhar-backed talks would happen very soon, while Mursi's Muslim Brotherhood signalled it was ready to take part as long as they were on the right terms.
Mursi's backers stood firm in protest camps in Cairo's al-Nahda Square and around Rabaa al-Adawiya mosque.
No police crackdown appeared imminent despite frequent warnings from the army-installed government that the protesters should pack up and leave.
Interim President Adli Mansour swore in at least 18 new provincial governors, half of them retired generals, reversing Mursi's appointment of civilians.
The "April 6" pro-democracy youth movement, which played a prominent role in the revolt that brought down long-time strongman Hosni Mubarak in 2011, was among those criticising the appointments as a step backwards.
"Holding on to the old faces that contributed to ruining political life before the revolution is a new failure for the current administration," it said on its website. (Writing by Angus MacSwan in Cairo; Editing by Mark Heinrich and Robin Pomeroy)