* Turkish PM will need Kurdish support to secure presidency
* Local elections strengthen his hand in peace process
* Advances could help ease relations with European Union
* Kurdish opposition says support depends on reforms
By Orhan Coskun and Gulsen Solaker
ANKARA, April 3 (Reuters) - Prime Minister Tayyip Erdogan will be banking on Kurdish support if he bids for Turkey's presidency in an August election and is likely to use his party's strong showing in local polls as a mandate to advance peace talks with Kurdish militants.
Erdogan's AK Party emerged well ahead of rivals in municipal elections on Sunday, increasing its share of the vote including in parts of the Kurdish-dominated southeast. The outcome has bolstered his hand in a peace process in which he has invested much political capital despite staunch nationalist opposition.
Erdogan has made no secret of his desire to run for Turkey's first directly-elected presidency in four months' time. But he could face a united front from opponents who fear his victory would exacerbate what they see as his growing authoritarianism.
Support from Kurds, Turkey's largest minority, accounting for around a fifth of the population, could see off that opposition and help give him the simple majority needed to win in a first round, Erdogan's advisers say.
"The local election results have brought him much closer to advancing the peace process and taking decisive steps. After this the process will accelerate, new concrete steps will be taken," a senior member of his office told Reuters.
"If Prime Minister Erdogan decides to be a candidate for the presidency, the Kurds will give him serious support."
Turkish officials launched peace talks with jailed Kurdish militant leader Abdullah Ocalan in late 2012 with the aim of ending a conflict which has killed more than 40,000 people and hampered development in the mainly Kurdish southeast.
Advances in peacemaking could re-enamour the European Union candidate nation to Brussels, critical of Erdogan's crackdown on street protests last summer, as well as moves including a block on Twitter as he battled a corruption scandal in the run-up to Sunday's elections.
The EU would find it hard to turn its back if Ankara made progress on one of its most pressing issues, diplomats said.
The AK Party won around 45 percent of the vote in Sunday's municipal elections, widely seen as a referendum on Erdogan's rule after last summer's protests and the graft scandal, while the pro-Kurdish BDP and an allied party took around 6 percent.
Time for Erdogan to decide on whether to launch a presidential bid is fast running out. Incumbent President Abdullah Gul, seen as a potential future prime minister should Erdogan win the presidency, expects a decision within weeks.
"This will become clear by the end of April or the start of May," the Hurriyet newspaper quoted him as telling reporters during a visit to Kuwait.
NO FOREGONE CONCLUSIONS
Whatever other reservations Turkey's Kurds may have about Erdogan, he is widely seen as the only modern leader strong enough to have advanced a peace process with militant Kurds long unthinkable in a country where nationalist sentiment runs deep.
Ocalan, jailed on the island of Imrali south of Istanbul, called a ceasefire in March last year and it has largely held. However, his Kurdistan Workers Party (PKK) militants halted their withdrawal to bases in the mountains of northern Iraq in September in protest at what it saw as slow progress on reforms.
During its 11 years in power, the AK Party has pushed through reforms boosting Kurdish linguistic and cultural rights.
But Kurdish support for Erdogan's candidacy is not a foregone conclusion and the BDP and allied HDP party have not yet formally discussed the issue.
"If the government takes steps which satisfy the Kurds and meet their demands, the BDP and HDP may take significant steps in this regard. But for now it would not be right to say whether we support it or not," said senior BDP deputy Pervin Buldan.
She said her party would discuss the way forward with Ocalan himself in talks expected soon.
Buldan's party has presented a bill envisaging measures including the abolition of an anti-terror law which has been used against Kurdish activists, changes in the Turkish penal code and the release of detainees accused of links to the PKK.
Truces have been declared and secret talks held with the PKK in the past, but expectations this time have been swelled by the openness with which the process has been conducted. The path to disarmament and reintegration of militants in Turkish society nonetheless remains long.
Opposition to a closer marriage of convenience with Kurdish parties could undermine support for Erdogan among the more nationalist segments of his conservative support base.
"The BDP is not helping the AK Party as a goodwill gesture," said Hurriyet Daily News editor Murat Yetkin, noting the BDP has pledged to take steps towards building Kurdish autonomy in the provinces it controls following the elections.
The civil war in neighbouring Syria, where a group aligned with the PKK wields considerable power much to the consternation of Ankara, could also hamper efforts to advance the process.
Disputes over some of Sunday's elections have also created a hurdle. The PKK decried what it said had been tampering with ballot boxes, the stealing of voting slips and the drafting in of soldiers and state employees to vote in mainly Kurdish areas.
"Our people's resistance against the anti-democratic, repressive and fascist attacks of the AKP is a legitimate one," it said in a statement, and its sympathisers would not recognise disputed mayors. The PKK warned of potential "reprisals". (Additional reporting by Ayla Jean Yackley; Writing by Daren Butler; Editing by Nick Tattersall/Mark Heinrich)