* Turkey opens push west of Jarablus
* Tanks enter al-Rai to support offensive
* Turkey-backed rebels take villages to east of al-Rai (Adds air strikes on Saturday, comments from Erdogan interview)
By Umit Ozdal and John Davison
ELBEYLI, Turkey/BEIRUT, Sept 3 (Reuters) - Turkey and its rebel allies opened up a new line of attack in northern Syria on Saturday as Turkish tanks crossed the frontier from Kilis province, making a western thrust in an operation to sweep militants from its border.
The incursion from Kilis - which has been repeatedly targeted by Islamic State rockets from inside Syria over the last year - coincided with a push elsewhere in the region by the Turkish-backed Syrian rebels, who seized several villages further east from the Sunni hardliners.
By supporting the rebels, mainly Arabs and Turkmen fighting under the loose banner of the Free Syrian Army, Turkey is hoping to push out Islamic State militants and check the advance of U.S.-backed Syrian Kurdish fighters.
The rebels last week took the frontier town of Jarablus with Turkish support. The operation, called Euphrates Shield, is Ankara's first full-scale Syrian incursion since the start of the five-year-old war.
On Saturday the tanks crossed the border and entered the Syrian town of al-Rai to support the new offensive, a rebel spokesman and monitors said. Now under rebel control, al-Rai had previously been in the hands of Islamic State.
Al-Rai is about 55 km (34 miles) west of Jarablus, and part of a 90-km corridor near the Turkish border that Ankara says it is clearing of jihadists and protecting from Kurdish militia expansion.
A rebel commander said they would aim to push east from al-Rai, in the direction of Jarablus, which would put pressure on Islamic State from both east and west of a stretch of territory it controls along the border between the towns.
"The operations are to work from al-Rai towards the villages that were liberated to the west of Jarablus," Colonel Ahmed Osman of the Sultan Murad rebel group told Reuters, adding that the offensive was backed by Turkey.
The Hamza Brigade, part of the Free Syrian Army, said it had taken control of Arab Ezza, a village about 30 km west of Jarablus and near where Turkish warplanes carried out air strikes on Friday.
FSA factions had also captured the villages of Fursan, Lilawa, Kino and Najma just south of Arab Ezza, a source in the Failaq al-Sham rebel group said.
U.S. forces hit Islamic State targets overnight near Turkey's border with Syria.
"U.S. forces struck ISIL targets near Turkey's border in Syria last night via newly deployed HIMARS system," Brett McGurk, the special presidential envoy for the coalition fighting Islamic State, said on his Twitter account.
HIMARS refers to a High Mobility Artillery Rocket System. It was not immediately clear where at the border the system had been deployed.
Turkey's pro-government Daily Sabah newspaper said Turkish air strikes in support of the rebels continued on Saturday.
FOCUS ON KURDISH MILITIA
While Euphrates Shield initially targeted Islamic State in Jarablus, most of the focus since has been on checking the advance of U.S.-backed Syrian Kurdish fighters, to the alarm of NATO ally Washington.
Turkey disagrees with its ally's support for the Syrian Kurdish YPG militia, which it considers a terrorist group. The YPG has been among the most effective partners on the ground in the U.S.-led fight against IS.
Turkey is worried that advances by Syrian Kurdish fighters will embolden Kurdish militants in its southeast, where it has been fighting an insurgency for three decades led by the outlawed Kurdistan Workers Party (PKK).
In China, to attend the G20 meeting of world leaders, President Tayyip Erdogan said there should be no support for any terrorist organisation - a reference to the United States' backing of the Syrian Kurdish fighters.
"There is no good terrorist. All terrorists are bad. All organisations involved in terrorism are cursed. This is how we see things and how we put up our struggle," he said, according to a transcript of an interview with China's CCTV released by Erdogan's office.
The United States has voiced concerns about Turkish strikes on Kurdish-aligned groups that Washington supports. Germany said it did not want to see a lasting Turkish presence in an already tangled conflict.
Turkey has said it has no plans to stay in Syria and simply aims to protect its frontier from the militant group and the Kurdish YPG militia.
Activists have reported protests in some Syrian towns near the Turkish border in recent days against what demonstrators have called Turkish imperialism. Turkish security forces used tear gas and water cannon to disperse protesters along the border on Friday. (Additional reporting by Yesim Dikmen and Asli Kandemir in Istanbul, Tom Perry in Beirut and Suleiman Al-Khalidi in Amman, Writing by David Dolan, Editing by Andrew Bolton and Angus MacSwan)