Turkish president Recep Tayyip Erdogan said on Monday an offensive against a US-backed Kurdish militia in Syria would be unrelenting, revealing Russia backed the operation.
Troops continued to shell militia targets in the Kurdish-held Syrian enclave of Afrin, claiming progress in a cross-border offensive.
"We are determined. Afrin will be sorted out. We will take no step back. We spoke about this with our Russian friends. We have an agreement," Mr Erdogan told a televised meeting in Ankara.
The operation, called Olive Branch, was launched on Saturday with Turkish war planes and artillery preceding a major ground incursion involving Ankara-backed rebels and Turkish tanks.
Its aim is to oust from Afrin the People’s Protection Units (YPG) militia, which Turkey considers to be a terrorist organisation and linked to the Kurdistan Workers’ Party (PKK) that has waged a three-decade insurgency against the Turkish state.
But the operation is hugely sensitive as Washington relied on the YPG, the backbone of the US-backed Syrian Democratic Forces (SDF) alliance, to oust ISIL from its Syrian strongholds.
The Associated Press reported that a Turkish soldier was killed as the country pressed its offensive against Kurdish militia targets in northern Syria, the army said, confirming the operation's first Turkish fatality on its third day.
“One of our heroic soldiers was martyred during clashes” with Kurdish militants from the People’s Protection Units (YPG) militia southeast of the Turkish border town of Gulbaba in Kilis on Monday, the Turkish army said in a statement.
Away from the battlefield, Russia announced on Monday that yet another round of Syrian peace talks will take place in the Black Sea resort of Sochi on January 29 and 30.
The talks will focus on drafting a new constitution for post-war Syria with support from regime backer Iran and rebel backer Tukey.
Russian foreign minister Sergy Lavrov said Kurdish representatives had been invited to take part in the talks despite the continuing Turkish offensive in northern Syria.
Meanwhile, a Kurdish news agency said Turkey's military was also targeting Kurdish forces in eastern Syria, hundreds of miles from Afrin.
Hawar said Kurdish fighters returned cross-border fire in the northeastern province of Hassakeh, a predominantly Kurdish area bordering Iraq.
A Turkish official in southwestern Turkey could not confirm the report, but the Syrian Observatory for Human Rights, a Britain-based monitoring group, also reported skirmishes in Hassakeh.
France has called for an emergency UN Security Council meeting to take place on Monday to discuss concerns over flashpoint areas in Syria, including the Ankara operation. Meanwhile, British prime minister Theresa May said the UK would look into ways to stop further escalation of violence in Syria.
"We recognise Turkey has a legitimate interest in the security of its borders," a spokesman for Mrs May said.
"The UK is committed to working closely with Turkey and other allies to find solutions that provide stability, refrain from escalating the situation and protect Turkey's security interests."
Read more: Turkish special forces and allied militias capture villages in Kurdish enclave
Turkish television quoted military sources as saying the ground forces had already taken 11 villages in their advance into Syria.
The Britain-based Syrian Observatory for Human Rights said a total of 21 civilians - including six children - had been killed in the operation.
But Ankara has denied inflicting civilian casualties, with foreign minister Mevlut Cavusoglu accusing the YPG of sending out "nonsense propaganda and baseless lies".
The SDF said on Monday that it was studying the possibility of sending reinforcements to Afrin.
"We are in the framework of looking at the possibility of sending more military forces to Afrin," SDF spokesman Kino Gabriel said in a televised news conference, calling for international efforts to halt the Turkish attack.
He also said that the Turkish offensive was “clear” support for ISIL.
On Sunday, Mr Erdogan said he believed the operation will end “in a very short time”.
Deputy prime minister Mehmet Simsek said the operation would be short and would not have a negative effect on the economy.
"Investors should be calm," he said. "This will be an effective, and limited operation and, God willing, it will be short."
In a sign of the risks to Turkey, 11 rockets fired from Syria hit the Turkish border town of Reyhanli on Sunday, killing one Syrian refugee and wounding 46 people, 16 of them Syrian, the local governor said.
The operation is Turkey's second major incursion into Syria during the seven-year civil war after the August 2016 to March last year Euphrates Shield campaign in an area to the east of Afrin, against both the YPG and ISIL.
Read more: Turkey is deploying anti-terror rhetoric to settle old scores against the Kurds
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 ISIL after a string of successes in recent months.
In its first reaction, the US state department urged Turkey "to exercise restraint" and ensure the operation remained "limited in scope".
Defence secretary Jim Mattis said Turkey had been "candid" and had provided Washington with advance warning of its operation.
The UAE also expressed concern over the recent developments in northern Syria, calling for a new Arab national security framework.
“The developments pertaining to Afrin reaffirm the need to work on rebuilding and restoring the concept of Arab national security on a realistic and modern basis,” Dr Anwar Gargash, UAE's Minister of State for Foreign Affairs, tweeted late on Sunday.
“Without that, Arabs will be marginalised and their homes an [exposed] public domain.”
Mr Erdogan has urged national solidarity over the operation and the government has reached out to leaders of the main nationalist and secular opposition parties.
But Mr Erdogan warned those who respond to calls by the pro-Kurdish Peoples' Democratic Party (HDP) for protests will have to pay a "heavy price".
The authorities on Monday detained 24 people on suspicion of disseminating "terrorist propaganda" in favour of the YPG and against the operation on social media.
Turkish anti-riot police on Sunday blocked protests in Istanbul and in Diyarbakir against the Syria offensive.