In a statement on its official Telegram channel, the RSF said the clashes "resulted from an unintentional mistake during field operations" targeting forces from the Sudanese army who had entered from Chadian territory "to stir discord and then fled back" into Chad.
Sudan has been gripped by conflict since April 2023. Fighting between the army and the RSF has killed tens of thousands of people and displaced 11 million.
Around one million Sudanese refugees have fled to Chad, according to the United Nations.
The RSF said it respected Chad's sovereignty and internationally recognised borders and was committed to "continuing ongoing investigations" and "taking the necessary measures" to hold those responsible accountable.
Chad's government had earlier blamed the RSF for the violence.
Government spokesman Gassim Cherif told a news conference that armed fighters from Sudan had crossed into Chad on Thursday, prompting a clash when Chadian troops ordered them to leave.
A government official later told AFP that the Sudanese fighters were "RSF elements".
Sudan's army has repeatedly accused the United Arab Emirates of supplying weapons to the RSF and hiring mercenaries routed through Chad, Libya, Kenya or Somalia -- claims denied by Abu Dhabi.
Border tensions have risen since October, when the RSF seized El-Fasher, the army's last stronghold in Darfur, prompting international condemnation over reports of mass killings, summary executions and systematic rape.
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