Chadian government spokesman Gassim Cherif told a news conference there had been an "incursion" into Chad on Thursday by armed fighters from Sudan, leading to a clash when Chadian troops ordered them to leave.
A government official told AFP the Sudanese fighters were "RSF elements".
The RSF's war with the Sudanese army has killed tens of thousands of people and forced some 12 million from their homes since it erupted in April 2023.
Around one million Sudanese refugees have fled to Chad, according to the United Nations.
On December 26, two Chadian soldiers were killed at the border in a drone attack by the RSF.
Cherif said the latest clash had occurred near the border city of Tine.
"We call on all parties in the conflict to stop all violations of Chadian territory," he said.
"This is our final warning," he added.
"We cannot have our defence and security forces dragged into the conflict... or Chadians dying."
The United Arab Emirates, which has been accused of backing the RSF, condemned the attack, but did not attribute it to the paramilitary group.
The RSF have staged several attacks near the Chadian border since October, when they seized the city of El-Fasher, the Sudanese army's last holdout position in the Darfur region.
That offensive triggered an international outcry over reports of mass killings, summary executions and systematic rape by the RSF.
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