* Turkey hits Islamic State, Kurdish militias in Syria

* U.S. worries by what it see as focus on Kurdish forces

* France says striking Kurdish groups may inflame conflict

(Recasts with comments from Turkish military, France, opposition)

By Edmund Blair and Asli Kandemir

ISTANBUL, Aug 30 (Reuters) - Turkey's army chief signalled no let up in a Syria offensive Washington has criticised for targeting U.S.-backed Kurdish fighters as well as jihadists, and said its successes showed last month's failed coup had not dented the military's power.

Turkish-backed forces began the offensive last week by capturing the Syrian frontier town of Jarablus from Islamic State; they then advanced on areas controlled by Kurdish-aligned militias which have U.S. support in battling jihadists.

Turkey, which is fighting a Kurdish insurgency at home, has openly said the operation dubbed "Euphrates Shield" has a dual goal of driving away Islamic State and preventing Kurdish forces extending their areas of control along the Turkish border.

Washington said the offensive by its NATO ally risked undermining the fight against Islamic State because it was focusing on Kurdish-aligned militias. Ankara says it will not take orders from anyone on how to protect the nation.

"By pursuing the Euphrates Shield operation, which is crucial for our national security and for our neighbours' security, the Turkish Armed Forces are showing they have lost none of their strength," Chief of General Staff Hulusi Akar said in a statement on Tuesday to mark a national holiday.

On the eve of the Victory Day holiday, President Tayyip Erdogan said the operation would continue until all threats, including that of Kurdish militia fighters, were removed from the border area.

Turkey is still reeling from an attempted coup in July in which rogue military commanders used warplanes and tanks to try to oust Erdogan and the government, exposing splits in the ranks of NATO's second biggest military.

In a subsequent purge of suspected coup sympathisers, 80,000 people have been removed from both civilian and military duties, including many generals, officers and rank-and-file soldiers.



FLARE-UP

Echoing U.S. concerns about the Turkish offensive in Syria, French President Francois Hollande said he understood Turkey's need to defend itself from Islamic State but that targeting Kurdish forces which were battling jihadists could further inflame the five-year-old Syrian conflict.

"Those multiple, contradictory interventions carry risks of a general flare-up," he told a meeting of French ambassadors.

Criticism by any Western powers will add to tensions with Ankara, which has accused the United States and Europe of proving poor allies by calling for restraint as the government rounded up coup sympathisers, and failing to appreciate the depth of the threat the coup presented to Turkey's democracy.

U.S. Vice President Joe Biden visited Ankara last week to try to patch up ties and voice support for the government. But this week, U.S. officials described the current direction of the offensive as "unacceptable".

In its northern Syria offensive, Turkish forces and their rebel allies have taken a string of villages in areas controlled by the Kurdish-aligned Syrian Democratic Forces (SDF) and advanced towards Manbij, a city the SDF seized from Islamic State this month in a U.S.-backed campaign.

Turkey says its forces have struck multiple positions held by the Kurdish YPG militia, part of the SDF coalition.

The YPG says its forces withdrew from the region before the Turkish assault and have already crossed the Euphrates, in line with a demand from the United States to withdraw to the eastern side of the river that flows through Syria or lose U.S. support.

Turkey wants to stop Kurdish forces taking control of territory that lies between cantons to the east and west that they already hold, and so creating an unbroken Kurdish- controlled corridor on Turkey's southern border.

(Additional reporting by Andrew Callus and John Irish in Paris, David Dolan and Nick Tattersall in Istanbul; Writing by Edmund Blair; Editing by Nick Tattersall and Ralph Boulton) ((edmund.blair@thomsonreuters.com; Reuters Messaging: edmund.blair.thomsonreuters.com@thomsonreuters.net))