"We absolutely reject this language ... addressed to individuals," a separate statement, issued by the SDF command, said. "The Syrian Ministry of Defence should have addressed its speech to the General Command of the Syrian Democratic Forces in order to open the door for dialogue first."
The Syrian Defence Ministry had said the army was "ready to receive SDF members and units who are willing to join it."
"We in Syria are facing a common enemy, and the people of unified Syria from the Arabs and Kurds must sacrifice to restore every inch of the beloved Syrian territories," it said in a statement.
Turkey launched its incursion into north-eastern Syria on October 9 to push back Syrian Kurdish militias, which lost more than 10,000 people fighting alongside the US against Islamic State.
A controversial US decision to pull forces from the region paved the way for the Turkish invasion.
The SDF, which has controlled swathes of north-eastern Syria, is mainly led by the People's Protection Units (YPG). Ankara considers the YPG to be linked to the Kurdistan Workers' Party (PKK), a designated terrorist group fighting an insurgency on Turkish soil.
Two ceasefire deals, first with the United States and then with Russia, brought a pause to the fighting in north-eastern Syria and were intended to allow Syrian Kurdish fighters to evacuate the border area.
On Tuesday, Syrian government troops clashed for the first time with Turkish-backed rebels in the region, the Syrian Observatory for Human Rights said.
Meanwhile, Turkish President Recep Tayyip Erdogan confirmed that Turkey and Russia will begin joint patrols in north-eastern Syria on Friday.
But he warned on Wednesday that Syrian Kurdish militias hadn't fully withdrawn from a 30-kilometre-deep zone from Turkey's border with Syria in keeping with a deal struck between Ankara and Moscow.
"We reserve the right to start our own offensive," Erdogan said, if attacks against Turkey continue.
On Tuesday, Russian Defence Minister Sergei Shoigu confirmed the complete withdrawal of Syrian Kurdish forces.
But Fahrettin Altun, Erdogan's communications director, said: "We will establish, through joint patrols, whether or not the terrorists have actually withdrawn."
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