"They will continue investigation activities until tomorrow Friday and they will come out of Syria by Saturday morning and will report to me as soon as they come out," Ban told journalists.
The UN chief also said he had spoken yesterday to US President Barack Obama, as the United States appears to be moving closer to a military strike.
"I... Expressed my sincere wish that this investigation team should be allowed to continue their work as mandated by the member states," Ban said.
Ban has repeatedly spoken out against military action in Syria.
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But while he called for peace, he also urged those who may have used chemical weapons to be held responsible.
"Diplomacy should be given a chance... Peace (should) be given a chance," he said.
He added: "The use of chemical weapons by anyone, for any reason, under any circumstances, is a crime against humanity and that must be held accountable for."
A team of UN inspectors has been investigating this week an alleged poison gas attack near Damascus on August 21, that the Syrian opposition says may have killed hundreds.