Turkey on Monday intensified its offensive against Kurdish militia targets in Syria as President Recep Tayyip Erdogan vowed there would be no stepping back in a campaign that has stoked concern among Ankara's allies and neighbours.

The Turkish military on Saturday launched operation "Olive Branch", its second major incursion into Syrian territory during the seven-year civil war.

The operation, where Turkish war planes and artillery are backing a major ground incursion launched with Ankara-backed Syrian rebels and Turkish tanks, aims to oust the People's Protection Units (YPG) militia from its enclave of Afrin.

Turkey considers the YPG to be a terror group and the Syrian offshoot of the Kurdistan Workers' Party (PKK) which has waged a bloody three-decade insurgency against the Turkish state.

"We are determined. Afrin will be sorted out. We will take no step back," Erdogan said in a televised speech in Ankara, adding that Russia had given its backing.

But the operation is hugely sensitive as Washington relied on the YPG to oust Islamic State (IS) jihadists from their Syrian strongholds and the Kurdish militia now holds much of Syria's north.

France has called for a UN Security Council meeting Monday to discuss concerns over flashpoint areas in Syria including the Turkish offensive.

- 'A short operation' -

State-run news agency Anadolu said ground forces had already taken 15 villages and other locations in their advance into Syria. Prime Minister Binali Yildirim said since Saturday 170 targets had been destroyed.

Meanwhile, Turkish artillery fired shells on YPG targets inside Syria and ground troops opened a new front by moving on Afrin from the town of Azaz to the east, state media said.

The Britain-based Syrian Observatory for Human Rights said a total of 21 civilians -- including six children -- had been killed in the operation. It said 13 Ankara-backed rebels were killed and 9 Kurdish fighters.

But Ankara has denied inflicting civilian casualties, with Foreign Minister Mevlut Cavusoglu accusing the YPG of sending out "nonsense propaganda and baseless lies".

Observatory director Rami Abdel Rahim told AFP in Beirut that the clashes were the fiercest since the start of the offensive. Turkey-backed forces had also taken a key hill in Afrin, both he and Anadolu said.

An AFP correspondent in the Turkish border village of Hassa saw more Turkish tanks heading towards Syria, enthusiastically cheered by locals.

In a sign of the risks to Turkey, rockets fired from Syria on the border town of Reyhanli on Sunday killed one Syrian refugee. One more person was killed in a similar attack Monday on the village of Kirikhan.

Yildirim said that the Turkish army had suffered no losses.

The Syrian Democratic Forces, an umbrella group dominated by the YPG, said in a statement that the operation amounted to "clear support" for IS.

The operation is Turkey's second major incursion into Syria during the seven-year civil war after the August 2016-March 2017 Euphrates Shield campaign in an area to the east of Afrin, against both the YPG and IS.

Erdogan has warned that those protesting against the operation will have to pay a "heavy price" and Turkish police detained 24 people on suspicion of disseminating "terror propaganda" against the operation on social media.

- 'Russian backing' -

But as well as a complex military task, Turkey has to wage a sensitive diplomatic campaign to avoid alienating allies and provoking foes.

Western capitals are particularly concerned that the campaign against the YPG will take the focus away from eliminating IS after a string of successes in recent months.

US Secretary of State Rex Tillerson said Monday he was "concerned" about the offensive, saying the United States was in Syria with the aim of defeating the jihadists.

But Erdogan expressed impatience with US demands to set a clear timetable, saying the campaign would be over "when the target is achieved".

"How long have you been in Afghanistan? Is that over in Iraq?" he said, referring to the current US military presence in those countries which began with 2001 and 2003 invasions.

Erdogan has previously indicated that once control is imposed onto Afrin, Turkey wants to head west to defeat the YPG in the town of Manbij to the west.

Meanwhile Russia and Iran -- who have a military presence in Syria and are working with Turkey on a peace process -- have also expressed concern.

Erdogan insisted Turkey had discussed the operation in advance with Russia, and Moscow was in "agreement".

A crucial factor will be if the operation affects a Syrian peace conference to be held in the Russian resort of Sochi in late January.

Russian Foreign Minister Sergei Lavrov said Monday that Kurdish representatives would be invited, without specifying who, and accused the US of encouraging separatism among Syrian Kurds.