(Adds protests in Istanbul, Ankara)
By Ayla Jean Yackley
ISTANBUL, March 1 (Reuters) - Turkey's parliament has voted to close private preparatory schools, many of which are a source of income and influence for an Islamic cleric accused by Prime Minister Tayyip Erdogan of covertly seeking to topple him.
Lawmakers late on Friday set a deadline of Sept. 1, 2015, to shut the schools, news channels reported. Millions of students prepare at the centres for entrance examinations to win limited spots at state high schools and universities.
Erdogan has accused cleric Fethullah Gulen, whose followers wield influence in the police and judiciary, of concocting a graft scandal to compromise his government. The scandal broke with police raids on Dec. 17, but ties between the ex-allies have been tense in recent years.
"Pull your kids out, if they go to these schools. State schools are enough," Erdogan told a campaign rally before a March 30 election in the western town of Denizli on Saturday.
"They have sucked like leeches. Leeches are more virtuous: leeches suck dirty blood, while they suck clean blood and hold sessions cursing me, my wife, my children, my administration."
The government moved to shut down the cram centres in November, worsening the public row with Gulen's followers.
The local election next month is seen as a critical test of support for Erdogan after 11 years in power.
Last week, audio recordings purportedly of Erdogan and his son Bilal discussing moving large sums of money and accepting bribes were leaked on the Internet.
Erdogan has said the audio was manipulated, and on Saturday suggested Gulen was behind the "conspiracy".
"Listening to my phone is forbidden. They listened to me, the president, my family," Erdogan said at the rally.
"Now they've been caught. We are going into their lairs. It will take time but we will begin a new era with the votes we win on March 30."
Police used tear gas to disperse anti-government protests in Istanbul and the capital Ankara. Such demonstrations have become frequent occurrences in city centres in the last few weeks.
Riot police chased dozens of protesters in a residential area near Istanbul's Taksim Square. Undercover police grabbed some of them, handcuffed them and took pictures of them.
Education is central to the mission of U.S.-based Gulen's Hizmet, or Service, movement. Its respected prep schools help spread influence across a nationwide network, and shutting them will deprive Hizmet of a chief source of financing.
Followers of Gulen, who preaches respect for science, democracy and dialogue with other faiths, have forged a powerful socio-religious community network.
Gulen, who lives in self-imposed exile in Pennsylvania, says he has no plans to form a political party and denies any involvement in the graft investigation.
Erdogan, a devout Muslim whose AK Party traces its roots to political Islam, remains Turkey's most popular politician.
In parliament he faces a weak opposition and, supporters argue, at the polling stations his success in driving the economy could eclipse any damage from corruption accusations.
Erdogan has said abolishing the cram schools is part of a larger reform of an "unhealthy" educational system that ranks Turkey below the Organisation for Economic Cooperation and Development average in literacy, maths and science.
The law allows some of the cram schools to become private schools, giving them free access to properties that belong to the Treasury, and for the Education Ministry to recruit some of the teachers to work in public schools. (Additional reporting by Nicholas Tattersall and Seda Sezer; Editing by Ralph Boulton and Alistair Lyon)