Turkey said it was investigating the claims but insisted the Syrian Kurdish units remained “outside the scope of the current military effort”.
Turkey launched air raids on Islamic State fighters in Syria and positions of the Kurdish militant PKK in Iraq following violent attacks in Turkey.
Turkey has also said it has no plans to send ground troops into Syria.
The Kurdish People’s Protection Units (YPG), the armed wing of the main Syrian Kurdish party (PYD), said that Turkish tanks had shelled the Kurdish-held village of Zormikhar inside Syria late on Sunday evening.
It added that, an hour later, one of its vehicles had come “under heavy fire from the Turkish military east of Kobane in the village of Til Findire”.
“We urge Turkish leadership to halt this aggression and to follow international guidelines. We are telling the Turkish Army to stop shooting at our fighters and their positions.”
A Turkish government official said its military operations sought “to neutralise imminent threats to Turkey’s regional security” and was targeting IS in Syria and the Kurdish separatist PKK in Iraq.
“We are investigating claims that the Turkish military engaged positions held by forces other than [IS],” the official said.
“The PYD, along with others, remains outside the scope of the current military effort.”
Turkish Prime Minister Ahmet Davutoglu told a meeting of Turkish newspaper editors that, following Turkey’s military action, there were now “new conditions” in the regional conflict.
Such a deal would significantly increase the scope and pace of the US-led air war against IS in northern Syria, the paper says.
Nato is to hold an emergency meeting on Tuesday to discuss the situation.
Turkey – a Nato member – asked for the meeting based on Article 4 of the organisation’s founding treaty, which allows members to request such a summit if their territorial integrity or security is threatened.
“When Turkey requests for such a meeting I think it’s very right and very timely to have a meeting where we address the turmoil and the instability we see in Syria, Iraq and surrounding and close to Nato borders of Turkey,” Nato Secretary General Jens Stoltenberg told the BBC.
Mr Davutoglu said Turkey was prepared to work with the PYD – which has links to the PKK (Kurdistan Workers’ Party) – provided it did not pose a threat to Turkey and severed relations with Syrian President Bashar al-Assad.
However, the raids against the PKK in northern Iraq effectively ended a two-year ceasefire.
Monday: Thirty-two people are killed by IS-linked militants in the Kurdish-majority town of Suruc, near the border with Syria.
Thursday: IS forces shoot dead a Turkish border guard.
Meanwhile, the PKK reportedly kills two Turkish police officers in retaliation for Suruc and what it sees as Turkey’s collaboration with IS.
Friday: Hundreds of suspected IS supporters are arrested and properties are searched; Turkish F-16 jets bomb three IS targets in Syria.
Saturday: Turkey strikes IS and PKK targets in Syria and Iraq; the PKK says the conditions are no longer in place to observe a ceasefire.
Sunday: Car bomb attack on a military convoy in Lice in Diyarbakir provincekills two soldiers as strikes on targets in Iraq and Syria continue.
Turkish police have continued to arrest suspected members of IS or the PKK, with further early morning raids on Monday.
In recent days, Turkey has arrested hundreds of people suspected of supporting the militants.
Police raids on suspected IS and PKK members in the city of Istanbul triggered three days of rioting in the Gazi district.
At least one activist and a policeman have been killed.