Turkish ground troops have crossed into northern Syria as part of Ankara's campaign to rid the border area of Kurdish fighters, Turkey's PM says.
Binali Yildirim said the aim was to establish a 30km (19-mile) "safe zone" deep inside Syria, Turkish reports say.
Turkey launched its operation against Kurdish YPG militia in the Afrin region with air strikes on Saturday.
It risks increasing tensions with the US, which had supported the YPG in the fight against Islamic State jihadists.
The YPG has denied Turkish troops were on Afrin soil, saying they had "repelled" the attacks and forced them to retreat.
The Turkish military says it has so far taken out 153 targets belonging to Kurdish militants, while Kurdish rockets hit the border town of Kilis overnight.
The YPG (Syrian Kurdish People's Protection Units) is part of a US-backed alliance with a number of ethnic Arab militias called the Syrian Democratic Forces (SDF). The SDF has said it will have no choice but to defend itself if attacked.
What is happening in Afrin?
On Saturday, Turkey announced that an air and ground campaign, dubbed "Olive Branch", had been launched at 14:00 GMT, targeting the YPG and Islamic State (IS) group jihadists.
The operation would be carried out "with respect for Syria's territorial integrity", it added.
Pro-Turkey rebels, known as the Free Syrian Army, have also begun moving into the area, according to the state-run Anadolu news agency.
The YPG said the strikes had killed at least six civilians and three fighters, with another 13 civilians wounded. One of the fighters belonged to the YPG and the other two were from its all-female affiliate, spokesman Birusk Hasaka said.
Ankara also said there were casualties, but they were all Kurdish militants.
Prime Minister Yildirim was quoted by Turkish media as saying ground forces joined the operation by crossing into YPG-controlled territory on Sunday morning.
He gave no details about the 30km security zone troops are aiming to set up.
The YPG denied the reports. "All the Turkish military's ground attacks against Afrin have been repelled so far and they have been forced to retreat," said Nouri Mahmoudi, a spokesperson for the group.
Turkey's military has been shelling the region since Thursday, a move which it said was in response to fire coming from the area.
Risks of opening new front 'huge'
Mark Lowen, BBC Turkey correspondent, near border with Syria
In mid-afternoon on Saturday the Turkish air strikes began, with plumes of smoke rising above Afrin. On the ground, Syrian rebel fighters backed by Turkey moved in, the military incursion rather inappropriately named Operation Olive Branch.
President Erdogan has vowed to wipe out a corridor, first Afrin and then the nearby town of Manbij, from where the YPG has failed to withdraw. Nobody can object when what we do is necessary, he said. We will get rid of these messy terrorists trying to invade our country.
But the risks are huge – the offensive pits Turkey against its Nato ally the US, which backs the Kurdish militia against IS, infuriating Ankara. Russia, which has troops in the area, has urged restraint – an MP in Moscow says it will be discussed at the UN.
The Syrian regime warned it would be seen as a violation of Syria's sovereignty. An estimated half a million people have been killed in the Syrian war. With this new front, the danger is that number will rise again.
Why is Turkey targeting US-backed groups?
The YPG has been a key part of the battle against Islamic State in Syria, and has been supported by the US.
Turkey, however, believes the group has links to the banned Kurdistan Workers Party (PKK), and has for several months been threatening to clear Kurdish fighters from Afrin and another city, Manbij, which lies 100km away.
Turkey's military plans seem to have been accelerated by an announcement from the US that it will help the SDF alliance build a new "border security force" to prevent the return of IS.
The YPG and SDF deny any terrorist links – a claim backed by the US government.
But President Recep Tayyip Erdogan called the border force a "terror army".
The US state department has appealed for calm, and attempted to characterise the new development as security training.
How have Russia and the US reacted?
Russia's foreign ministry has said it is concerned by news of the offensive, and is urging restraint.
It said Foreign Minister Sergei Lavrov and his American counterpart Rex Tillerson had discussed "measures to take aimed at securing stability in the north of the country".
Russian senator Frants Klintsevich – who is the deputy chairman of the defence and security committee – told Interfax news agency that Moscow would only respond if Russian bases in Syria were threatened.
He said that Russia has been placed in a difficult situation, as it has "good relations with both Damascus and Ankara".
Turkey's military and intelligence chiefs had been trying to get Russia's agreement to allow Turkish planes to use the Russian-controlled airspace above Afrin.
Moscow is a key ally of Syrian President Bashar al-Assad and until now, had a contingent of soldiers at the airport in the centre of Afrin.
It is not yet clear if Russia's claim that it will not interfere precludes allowing use of its airspace.
Turkish Foreign Minister Mevlut Cavusoglu also discussed the military offensive with US Secretary of State Rex Tillerson.
No details of the conversations have been provided.