Marzuki Darusman told his sponsors in the UN Human Rights Council he was also still waiting for Myanmar's permission to enter the country, though he was hopeful there would be progress soon.
Darusman's team started its work in August, the month that attacks by Rohingya Muslim insurgents triggered a military response that has forced more than 410,000 Rohingya into neighbouring Bangladesh.
Myanmar has denied rights groups' accusations that it is trying to drive the minority community out of Rakhine state, saying it is only targeting militants.
Darusman told the Geneva-based council the time left until his current March 2018 deadline was "utterly insufficient" and asked for a six-month extension.
"Now facing an escalating situation in northern Rakhine that is increasing our workload exponentially, we are deeply concerned about our ability to verify the facts necessary to produce a report of the depth and quality that is expected of us by March."
Darusman said he was he hopeful there would be progress in his request to enter Myanmar, following an address by its leader Aung San Suu Kyi from which he said two main points emerged.
"One, the categorical readiness of the government of Myanmar to receive back returnees at any time on the basis of a procedure that will have to be discussed at some point.
And secondly, the readiness of the government to undertake be globally scrutinised by the international community.
These two points bode well."His mission is meant to assess the situation across all of Myanmar since 2011.
Myanmar's ambassador Htin Lynn told the Council that Myanmar was making efforts to restore peace, law and order and harmony.
"Proportionate security measures targeted only on terrorists are being taken to safeguard our state security, and to restore law and order," he said.
"We continue to believe that instituting such a mission is not a helpful course of action in solving the already intricate Rakhine issue with daunting challenges."
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