Turkey has threatened further intervention in northern Syria unless Kurdish-led forces fully withdraw east of the River Euphrates within a week.
On Wednesday, Turkish forces helped Syrian rebels take the border town of Jarablus from so-called Islamic State.
Turkish Defence Minister Fikri Isik said on Thursday the operation had two goals – to secure the border area and ensure the Kurds “are not there”.
Ankara fears Kurdish gains in Syria will fuel an insurgency at home.
As Mr Isik spoke, a column of some 10 Turkish tanks and a similar number of armoured vehicles reportedly crossed the border near Jarablus.
It was not immediately clear if the deployment was aimed at securing the town or helping members of the rebel Free Syrian Army push further into IS-held territory.
Rebel commanders said they had advanced up to 10km (6 miles) south of Jarablus and 10km westwards along the Turkish frontier.
Later in the day, the Turkish military shelled a group of Syrian Kurdish fighters near Manbij, south of Jarablus, Turkish media said.
The UK-based Syrian Observatory for Human Rights said fighters from the US-backed Syrian Democratic Forces (SDF), an alliance dominated by the Kurdish Popular Protection Units (YPG) militia, had moved north from positions near Manbij, which they recently captured from IS.
A rebel source told the Reuters news agency that the two sides had clashed at the village of al-Amarna, on the western bank of the Euphrates, on Wednesday night.
During a visit to Ankara on Wednesday, US Vice-President Joe Biden said Washington had warned the SDF not to move west of the Euphrates or risk losing American support.
Mr Isik told NTV television: “If this withdrawal doesn’t happen, Turkey has every right to intervene.”
Earlier, a spokesman for the US-led coalition against IS tweeted that SDF fighters had moved east across the Euphrates from Manbij to prepare for “the eventual liberation” of the IS stronghold of Raqqa.
Col John Dorrian subsequently issued a clarification, which said: “Main element of SDF Manbij liberation force has gone east; some forces remain to finish clearing, IED [Improvised Explosive Device] removal as planned.”
The YPG meanwhile said in a statement that the SDF had handed over military command in Manbij and all of its positions in the town to the local Manbij Military Council.
The BBC’s Mark Lowen, who is on the Turkish-Syrian border, says that getting the US to demand the SDF withdraw was a major diplomatic victory for Turkey, which has long felt that the Americans have prioritised collaboration with the Kurds in Syria over supporting their Nato ally.
The SDF has been the most effective opponent of IS on the ground in Syria and its fighters control an uninterrupted 400km stretch of the Syrian-Turkish border, from Iraq to the Euphrates, as well as an enclave around Afrin.
However, Turkey views the YPG as an extension of the Kurdistan Workers Party (PKK), a Turkish Kurdish rebel group fighting for autonomy since the 1980s.
In a separate development on Thursday, a convoy carrying opposition leader Kemal Kilicdaroglu was attacked in north-eastern Turkey.
The interior minister said three soldiers were wounded in an exchange of fire with the assailants, who he identified as PKK rebels. Later, the state-run Anadolu news agency reported that one of the soldiers had died of his wounds.
Mr Kilicdaroglu’s Republican People’s Party (CHP) said he was safe and well.
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Source: BBC