President Recep Tayyip Erdogan on Tuesday said Turkish forces would soon lay siege to Syria's Afrin as a cross-border offensive targeting a Kurdish militia entered its second month.

On January 20, Ankara launched an air and ground operation supporting Syrian rebels against the People's Protection Units (YPG) in the Afrin region of northern Syria.

Turkey views the YPG as a Syrian offshoot of the outlawed Kurdistan Workers' Party (PKK), which has been waging an insurgency against the Turkish state since 1984.

“In the coming days, swiftly, we will lay siege to the centre of the town of Afrin,” Erdogan told parliament.

While some analysts say Turkey and pro-Ankara Syrian rebels have made slow advances, Erdogan defended the operation's progress, saying the army wanted to avoid putting the lives of both its troops and civilians needlessly “at risk”.

“We did not go there to burn it down,” he said, adding that the operation's aim was to “create a safe and liveable area”, where Syrian refugees in Turkey could conceivably return to.

Since Syria's war erupted in 2011, more than 3.5 million people have sought refuge in Turkey.

According to the Syrian Observatory for Human Rights monitor, Syrian rebels and Turkish forces have taken 45 villages since the start of the operation, most of them bordering Afrin.

And Turkish security expert Abdullah Agar said troops involved in operation “Olive Branch” had captured around 300 square kilometres (120 square miles) of territory.

Over the past month, 205 Syrian rebels have been killed, along with 219 YPG and allied fighters and 112 civilians, Observatory figures show.

The Turkish army says 32 of its troops have been killed since the offensive was launched.

Ankara strongly denies there have been any civilian casualties.

Warning to Damascus

Jana Jabbour, a political science professor at Sciences Po university in Paris, said the Turks were “struggling to move forward” because of the “organisation of the Kurdish YPG forces and their combativeness”.

She said it was important to distinguish between political rhetoric, “even political propaganda”, and the reality on the ground.

On the ground, fighting was now focused around the area of Arab Wiran in northeast Afrin, the Observatory said.

If captured, pro-Ankara forces would control 50 continuous kilometres of Afrin's northern border with Turkey. The operation looked like it was going to be further complicated when Syrian state media reported that pro-government forces were expected to enter Afrin to counter the Turkish offensive.

In a thinly-veiled threat to Damascus, Erdogan on Tuesday warned Turkey would tolerate no interference. “We will block the way of those who come to help from outside the city or the region,” he said.

Later, Erdogan told reporters that the Syrian regime would not send any fighters.

Asked by a journalist if the regime backed down after Russian President Vladimir Putin and Erdogan spoke on the phone on Monday, the Turkish leader said without elaborating that the threat had been defused “after discussions”, NTV broadcaster quoted him as saying.

Strained ties with US

The operation strained already difficult ties with Washington, which has given weaponry to the YPG as part of its fight against Islamic State jihadists in Syria.

The US has called on Turkey to show restraint, warning that the offensive risks diluting the fight against the jihadists.

But instead of pulling back, Erdogan threatened to expand the offensive to the YPG-held town of Manbij. When US Secretary of State Rex Tillerson visited Ankara last week, the two sides agreed to work together in Syria and set up working groups on issues like Manbij where American troops are operating and which the US diplomat described as a “priority”.

In addition to its disagreements with Washington, Turkey must take into account the interests of Russia, a key Damascus ally, which controls northern Syrian airspace.

Moscow may have given the green light to the offensive, but it has previously closed the airspace to Turkish jets after a Russian plane was shot down in an area of north Syria where Turkish military observers were expected to enforce a de-escalation zone.

The offensive is broadly supported in Turkey where political parties, media and clerics speak in unison, against a backdrop of nationalist rhetoric led by Erdogan.

Only the pro-Kurdish Peoples' Democratic Party (HDP) does not back the operation.

Since Olive Branch got under way, Turkey has detained 786 people, 587 of whom are being held for spreading “terror propaganda” on social media, the interior ministry says, in what opponents charge is a crackdown on critics of the operation.

Another 85 people have been held on charges of organising protests against the offensive.