"That is ridiculous. I am perfectly fine," he said.
"I even had watermelon with this district chief on the way. I don't know why he is telling people that there was an ambush."
Rabbani said he was alerted to the "false" reports when he began receiving calls from around the world inquiring about his well-being.
While local media in Afghanistan have issued corrections, Salahuddin Rabbani, Burhanuddin Rabbani's son, gave a more detailed explanation of the events to Al Jazeera.
"There was an operation going on in the area by the Afghan National Army against the Taliban," he said.
"When my father's convoy passed through, the district chief, Habibullah Mohtashim, told my father and his convoy that they should wait five or 10 minutes because the operation was almost over and they were cleansing the area of the Taliban.
"So they waited and left. Habibullah himself has now said that this was false news propagated by Pajwak news agency."
Rabbani is a one of the main supporters of Abdullah Abdullah, the leading rival to incumbent Hamid Karzai, in the country's August 20 presidential poll.
Sources close to Rabbani said they believe that the report was a plot indirectly linked to the presidential campaign to make it appear as though the Abdullah camp has no support in Afghanistan's northern region.
"I don’t think anyone will benefit from this," Rabbani's son, a former counsellor at the permanent mission of Afghanistan to the UN from 2003 to 2006, said.
"Even the government itself will come under criticism because it shows them unable to bring security to the area."