One Turkish soldier was killed and three others injured on Saturday in an attack by Kurdish insurgents in Syria, Turkey's state Anadolu news agency reported.

The casualties are the first to be reported by Turkey since it started a military operation in northern Syria earlier this week.

Anadolu, citing a military official, said that the rocket attack was carried out by insurgents from the Kurdish Democratic Union Party (PYD), targeting two tanks.

Turkish forces "retaliated" with artillery fire, the official added.

Military helicopters transported the soldiers to hospitals in Turkey's Gaziantep province, according to the agency.

Earlier on Saturday, Turkish tanks advanced deeper inside Syria and clashed for the first time with powerful Kurdish-aligned forces who have been the United States' main ally against Islamic State extremists, according to a monitoring group and Kurdish sources.

The clashes took place after Turkish troops advanced on the village of Tel al-Amarna after subjecting it to shelling and airstrikes in the early morning, the Syrian Observatory for Human Rights said.

The Kurdish fighters destroyed three tanks belonging to the Turkish army and allied rebels during the fight, the Kurdish Hawar news agency reported without details.

The fighting came amid growing tensions after Turkey launched its first ground offensive inside Syria on Wednesday, backing up rebel forces that captured the border town of Jarabulus, 8 kilometres north of Tel al-Amarna, from Islamic State.

The Kurdish-led Democratic Forces of Syria (DFS), which had previously captured the nearby city of Minbij from Islamic State, has said that it is ready to defend Syrian territory against any "direct or indirect occupation."

Turkey says its operations are directed against both Islamic State and the PYD, which it regards as the Syrian branch of Kurdish rebels operating on its soil.

The Jarabulus Military Council, which is allied with the DFS, earlier said that Turkey had been attacking "our forces that are fighting against [Islamic State] groups." Syrian rebel groups were also fighting on the Turkish side, a Kurdish spokesman said.

Anadolu confirmed that Turkey had carried out strikes against an armoury and barracks belonging to an unnamed "terrorist organization" south of Jarabulus.

The DFS, dominated by the PYD's armed wing, has enjoyed US backing as the main force inside Syria to have fought against Islamic State.

Islamic State has controlled territory along the Syrian border since 2013. The Kurds, backed by US air power, began to push the group back in 2014, taking most of the border land.

After the Kurdish-led forces seized Minbij, west of the Euphrates River, this month from Islamic State, the last major town on the border under the extremists' control was Jarabulus, and a race developed between Turkey and the Kurds.

The US has said that the Kurds should hold off and retreat eastwards across the Euphrates, and that it would not back them with air power if they moved further west.

Turkey is a staunch backer of Syrian rebel groups fighting the government of President Bashar al-Assad and has moved hundreds of fighters into the Jarabulus region to fight Islamic State and the Kurds. Among the fighters are ethnic Turkmen brigades.

Syrian Turkmen leader Emin Bozoglan told Turkish media that the operation in Jarabulus is aimed at taking al-Bab, an Islamic State-held city near Aleppo.

The Kurds have also set their sights on al-Bab, which would allow them to link their main territory in north-eastern Syria to the north-western enclave of Efrin.

Turkey and Syrian rebels oppose such a link-up and also reject the autonomous region the Kurds have declared in the territories they control.

US Secretary of State John Kerry said late Friday in Geneva that the US had supported Kurdish fighters on a "limited basis" and remained in close coordination with Turkey.

"We are for a united Syria. We do not support an independent Kurd initiative," Kerry said.

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