Kurdish rebel fighters have begun leaving south-eastern Turkey for their safe havens in Iraq under a ceasefire, Kurdish sources say. "We know that they have started moving," Selahattin Demirtas, a pro-Kurdish politician involved in the peace process, told AFP news agency. The Kurdistan Workers' Party (PKK) announced last month a phased withdrawal to start early in May. More than 40,000 people have died in their 30-year fight against Turkey. Gultan Kisinak, who co-chairs the Peace and Democracy Party (BDP) along with Mr Demirtas, told the Associated Press news agency that a first group of fighters had started to move toward the border with northern Iraq. The PKK is believed to have up to 2,000 fighters inside Turkey and their full withdrawal may take several months. They are expected to cross the border on foot, heading for their bases in the Qandil Mountains of Iraq. Abdullah Ocalan, the veteran PKK leader in prison in Turkey, ordered the withdrawal in March as part of peace negotiations with Ankara. Withdrawal nerves According to AFP, PKK fighters complained on Tuesday that the Turkish state had increased its forces in the border area and was carrying out surveillance flights. Such actions, they said, were "delaying the peace process" and paving the way for "provocations and clashes". The Turkish army did not confirm any extra measures but said their "fight against any terrorism" continued. The PKK's acting leader, Murat Karayilan, warned in April that the fighters would strike back and the withdrawal would halt "immediately" if they were attacked. "We have no doubt about the state but fear provocation from dark forces," Mr Demirtas said. A 1999 withdrawal was abandoned after the Turkish military attacked rebels, killing some 500. In January, Prime Minister Recep Tayyip Erdogan pledged the army would not attack any PKK fighters who laid down their arms and agreed to withdraw from Turkish soil. "As you remember, there were some attempts [to withdraw] but [PKK militants] were shot down," he was quoted as saying by the Turkish newspaper Hurriyet. "But we can assure them that we will not permit similar incidents to occur. If they promise [to lay down arms] and leave our country, we acquiesce to them withdrawing from [Turkey] without any operations."