* Kurdish militants' protest enters 51st day
* Deaths possible after around 60 days, medical group says
* Erdogan dismisses hunger strike as a "show" (Adds statement from striking MP, comments from writer Yasar Kemal)
By Daren Butler
ISTANBUL, Nov 1 (Reuters) - Jailed Kurdish militants on hunger strike in Turkey may start to die within the next 10 days, Turkey's main medical association warned on Thursday, saying the prime minister's dismissal of the protest as a "show" risked hardening their resolve.
The hunger strike entered its 51st day on Thursday, with some 700 prisoners refusing food in dozens of prisons across Turkey, demanding the government grant greater Kurdish minority rights and better conditions for their jailed leader.
But the inmates are consuming sugar, water and vitamins that would prolong their lives and the protest by weeks.
The main demand of the protesters, mostly convicted members of the armed Kurdistan Workers Party (PKK) militant group, is improved jail conditions for PKK leader Abdullah Ocalan, imprisoned on an island in the Marmara Sea south of Istanbul.
The protests follow a surge in violence between Turkey and the PKK, which took up arms 28 years ago to try to carve out a Kurdish homeland in Turkey's southeast and which is designated a terrorist group by Ankara, the United States and European Union.
"Our worry is that after around 40 days lasting damage begins to emerge and after 60 days deaths may begin," Ozdemir Aktan, head of the Turkish Medical Association (TTB), which represents 80 percent of the nation's doctors, told Reuters.
Dozens of leftist prisoners died in a hunger strike more than a decade ago, but Prime Minister Tayyip Erdogan has played down the latest action, saying only one prisoner was on a "death fast" and was being monitored medically.
"Currently there is no such thing as a hunger strike. This is a complete show," he told reporters in Berlin on Wednesday.
He has said the inmates were being manipulated by "merchants of death", a reference to the PKK and Kurdish politicians, and accused Kurdish politicians of ordering the militants to go on strike while they themselves feasted on kebabs.
"Such statements make those taking part in hunger strikes more determined, motivating those who may have been considering giving up to continue. This can bring with it various illnesses and deaths," Aktan said.
"JOURNEY OF DEATH"
A jailed member of parliament from the pro-Kurdish Peace and Democracy Party (BDP), who joined the hunger strike on Oct 15, rejected Erdogan's description of the strike as a "show".
"We and hundreds of our friends are on a journey of death," Faysal Sariyildiz, member of parliament for the southeastern province of Sirnak, said from Diyarbakir prison where he is being held on remand on charges of links to the PKK.
"As much as hunger eats away at our bodies each day, the support of our people for the resistance is a big source of hope and morale for us," he said in a statement released by the BDP.
The hunger strike is another area of apparent difference between Erdogan and President Abdullah Gul, who have traded barbed comments in recent days over the police handling of a banned march.
One of Turkey's best known novelists, Yasar Kemal, called at a news conference in Istanbul for efforts to stop the protesters dying, saying the government was responsible for what happens as it had been in previous hunger strikes.
Aktan said the TTB had asked the justice ministry several times for permission to enter prisons and monitor the situation but had not yet received a response.
Authorities accepted such a request during a previous hunger strike in 2000 when 122 people died. That total includes 30 prisoners and two guards killed when security forces stormed jails to end the far-left protest against isolation in cells.
Hundreds more suffered permanent health damage and the TTB said inmates were again at risk from neurological illnesses such as Wernicke-Korsakoff syndrome, a condition whose symptoms include loss of memory and coordination.
Erdogan's government has introduced reforms granting greater Kurdish cultural rights since taking power a decade ago, but Turkey is also prosecuting hundreds of Kurdish lawyers, academics, activists and politicians on suspicion of PKK links.
More than 40,000 people have been killed since the militants took up arms in 1984 with the aim of carving out an independent state for Turkish Kurds, who now number around 15 million, or around a fifth of the population. (Additional reporting by Pinar Aydinli in Ankara; Writing by Daren Butler; Editing by Nick Tattersall and Jon Hemming)