IN A shiny office in the heart of Batman (see map), a group of men refuses to shake hands with female visitors, offering rosewater instead. They belong to Huda-Par, or “Party of Allah”, which was launched in December on a platform of Islamic values and greater rights for Turkey’s 14m mainly Sunni Kurds. Do they want sharia rule? Huseyin Yilmaz, Huda-Par’s deputy chairman, strokes his immaculately trimmed beard before responding. “We are Muslims before all else, but we will take note of the people’s wishes,” he says. “And the people will no doubt cleave to Allah’s path.” Huda-Par’s emergence might have been seen as part of the newly liberal atmosphere in the country’s war-wrecked, mainly Kurdish, south-eastern provinces. Instead, it has prompted worries of a fresh turf war between Islamist and nationalist Kurds. This risks undermining the ambitious (albeit bumpy) peace talks between the government in Ankara and rebels of the Kurdistan Workers’ Party (PKK). Many say the intra-Kurdish rivalry goes beyond a local quarrel and reflects tensions between Turkey and Iran. These, despite a recent flurry of official visits, continue to be inflamed by the war in Syria.

Huda-Par is closely linked to a shadowy militant group, Hizbullah, which has no connection with its Lebanese namesake but shares sympathy for Iran. Successive Turkish governments have long accused Iran of using Hizbullah as a fifth column to spread its ideology and to undermine Ataturk’s secular republic. In the 1990s Hizbullah was recruited by Turkey’s “deep state”, an allegedly antidemocratic group of senior spooks, military officers and members of the judiciary, to murder hundreds of PKK members and supporters. When Hizbullah carried its bloodletting beyond the south-east, the government began to clamp down, killing the group’s leader, Huseyin Velioglu, in a shoot-out in January 2000.

Even so, Hizbullah is “alive” and has made “a comeback with Huda-Par”, says Yilmaz Arslan, Batman’s governor. “Iran is using them to undermine Turkey and the peace process,” he adds.

Tensions between Huda-Par and the determinedly secular PKK have been bubbling ever since the Islamists announced they would be taking part in municipal elections in 2014. Last month the PKK accused Hizbullah of attacking mourners in the town of Cizre on the Iraqi border. In reply, Huda-Par complained that PKK vigilantes had repeatedly targeted its offices. “The PKK is scared of our popularity,” Mr Yilmaz insisted.

After PKK youths prevented Huda-Par volunteers from distributing leaflets on November 2nd, gunmen stormed a wedding attended by supporters of the pro-PKK Peace and Democracy Party (BDP), killing one guest. One of the assailants, who were arrested last week, was identified as a Huda-Par member and former Hizbullah militant.

“It is clear that Iran is behind them. Iran wants to stir things up,” claims Serhat Temel, Batman’s BDP mayor. This, he adds, is because of the PKK’s growing support among Iran’s own Kurds. Mr Yilmaz rejects the accusations, saying Iran is a convenient scapegoat for Turkey’s ills, but agrees that his party “respects the Iranian revolution”. Although the BDP is expected to sweep the local polls in the Kurdish region, Huda-Par is likely to lure away some pious Kurds. And its belated embrace of Kurdish nationalism has helped to boost its credentials.

On November 16th Recep Tayyip Erdogan, Turkey’s mildly Islamist prime minister, stole an electoral march against the BDP at a mass rally in Diyarbakir, its biggest stronghold. Flanked by Massoud Barzani, the leader of the semi-independent Kurdish statelet in northern Iraq, who is lauded by Kurds of all stripes, and Sivan Perwer, a Kurdish-nationalist singer, Mr Erdogan uttered the word “Kurdistan” for the first time. “We shall witness the days when those in the mountains [PKK rebels] will come down and the prisons will be emptied,” the prime minister roared.

BDP leaders have dismissed the rally as cheap electioneering. Mr Erdogan acknowledged this week that an amnesty for the rebels was not on the table.

Yet despite all the mutual recriminations, after 11 months of uninterrupted peace, neither side is ready to walk away. “The Kurds have finally tasted peace,” said Arif Arslan, the owner of an independent local newspaper. “Anyone who disrupts it, Huda-Par included, will be buried at the ballot box.”