* Turkey seeks to prevent Kurdish territorial gains

* Does not want Kurdish cantons unified in Syria

* Washington says Kurdish militia pulling back

(Adds Turkish defence minister, Syrian rebel advances, U.S. official)

By Humeyra Pamuk and Umit Bektas

KARKAMIS, Turkey, Aug 25 (Reuters) - Turkey sent more tanks into northern Syria on Thursday and demanded Kurdish militia fighters retreat within a week as it seeks to secure the border region and drive back Islamic State with its first major incursion into its neighbour.

Turkish special forces, tanks and warplanes on Wednesday entered Jarablus, one of Islamic State's last strongholds on the Turkish-Syrian border, in a U.S.-backed offensive. Gunfire and explosions echoed around hills in the region on Thursday.

President Tayyip Erdogan and senior government officials have made clear the aim of "Operation Euphrates Shield" is as much about stopping the Kurdish YPG militia seizing territory and filling the void left by Islamic State as about eliminating the radical Islamist group itself.

Turkey, which has NATO's second biggest armed forces, demanded that the YPG retreat to the east side of the Euphrates river within a week. The Kurdish militia had moved west of the river earlier this month as part of a U.S.-backed operation, now completed, to capture the city of Manbij from Islamic State.

Ankara views the YPG as a threat because of its close links to Kurdish militants waging a three-decade-old insurgency on its own soil. It has been alarmed by the YPG's gains in northern Syria since the start of the Syrian civil war in 2011, fearing it could extend Kurdish control along Turkish borders and fuel the ambitions of its own Kurdish insurgents.

Turkey's stance has put it at odds with Washington, which sees the YPG as an ally against Islamic State. It is one of the most powerful militias in Syria and regarded as the backbone of the Syrian Democratic Forces (SDF), a U.S.-backed alliance formed last October to fight the jihadist group.

Defence Minister Fikri Isik said preventing the Kurdish PYD party - the political arm of the YPG - from uniting Kurdish cantons east of Jarablus with those further west was a priority.

"Islamic State should be completely cleansed, this is an absolute must. But it's not enough for us ... The PYD and the YPG militia should not replace Islamic State there," Isik told Turkish broadcaster NTV.

"The PYD's biggest dream is to unify the western and eastern cantons. We cannot let this happen," he said.



EUPHRATES

U.S. Secretary of State John Kerry told Turkish Foreign Minister Mevlut Cavusoglu by phone on Thursday that YPG fighters were retreating to the east side of the Euphrates, as Turkey has demanded, foreign ministry sources in Ankara said.

A spokesman for the U.S.-led coalition against Islamic State also said the SDF had withdrawn across the Euphrates, but had done so "to prepare for the eventual liberation" of Raqqa, the radical group's stronghold in northern Syria.

Isik said the retreat was not yet complete and Washington had given assurances that this would happen in the next week.

"We are closely following this ... If the PYD does not retreat to east of the Euphrates, we have the right to do everything about it," he said.

Speaking during a visit on Wednesday to Turkey, U.S. Vice President Joe Biden also tried to soothe Turkish concerns about Kurdish territorial gains in Syria.

He said there should be no separate Kurdish entity in northern Syria and the country should remain united. Kurdish militia fighters would not receive U.S. support if they failed to pull back east of the Euphrates as promised, he said.

The offensive is Turkey's first major military operation since a failed July 15 coup shook confidence in its ability to step up the fight against Islamic State. It came four days after a suicide bomber suspected of links to the group killed 54 people at a wedding in the southeastern city of Gaziantep.

It comes at a testing time for Turkish-U.S. relations. Erdogan wants the United States to extradite Fethullah Gulen, a Turkish cleric who has lived in self-imposed exile in Pennsylvania for 17 years and whose religious movement he blames for staging last month's failed coup.

Washington says it needs clear evidence of Gulen's involvement and that it is a matter for the courts, a position that has sparked an outpouring of anti-Americanism from Turkey's pro-government media. Gulen denies any role in the coup attempt.



REBELS ADVANCE

The sound of gunfire, audible from a hill on the Turkish side of the border overlooking Jarablus, rang out early on Thursday and a plume of black smoke rose over the town. War planes flew overhead.

A senior Turkish official said there were now more than 20 Turkish tanks inside Syria and that additional tanks and construction machinery would be sent in as required. A Reuters witness saw at least nine tanks enter on Thursday, and 10 more were waiting outside a military outpost on the Turkish side.

"We need construction machinery to open up roads ... and we may need more in the days ahead. We also have armoured personnel carriers that could be used on the Syrian side. We may put them into service as needed," the official said.

Erdogan said on Wednesday that Islamic State had been driven out of Jarablus and that it was now controlled by Turkish-backed Syrian rebels, who are largely Arab and Turkmen.

"The myth that the YPG is the only effective force fighting Islamic State has collapsed," Erdogan's spokesman Ibrahim Kalin wrote on Twitter, reflecting Turkish frustration at how closely Washington has been working with the Kurdish militia.

Saleh Muslim, head of the Kurdish PYD, said on Wednesday that Turkey was entering a "quagmire" in Syria and faced defeat there like Islamic State. Redur Xelil, spokesman for the YPG, said the intervention was a "blatant aggression in Syrian internal affairs".

After seizing Jarablus, the Turkish-backed rebels have advanced up to 10 km (6 miles) south of the border town, rebel sources and a group monitoring the war said.

But the Syrian Observatory for Human Rights also said Kurdish-backed forces opposed by Ankara had gained up to 8 km of ground northwards, apparently seeking to pre-empt advances by the rebels. (Additional reporting by Orhan Coskun and Ece Toksabay in Ankara; Can Sezer, David Dolan, Cagan Uslu and Asli Kandemir in Istanbul, Tom Perry in Beirut; Writing by Nick Tattersall; Editing by Edmund Blair and Pravin Char) ((nicholas.tattersall@tr.com; Reuters Messaging: nicholas.tattersall.thomsonreuters.com@reuters.net))