"The whole process will be done strictly adhering to the highest established standards of verification recognised by the Organisation for the Prohibition of Chemical Weapons (OPCW)," Martin Nesirkysaid after a telephone call between Ban and Dr Ake Sellstrom, the head of the inspection team.
Ban asked Sellstrom to expedite the mission's analysis of the samples and information it had obtained "without jeopardizing the scientific timelines required for accurate analysis and to report the results to him as soon as possible," Nesirkysaid, adding that they had discussed ways to further accelerate the analysis.
He reiterated that the UN mission is "uniquely capable of establishing, in an impartial and credible manner, the facts of any use of chemical weapons based directly on evidence collected on the ground."
Syrian opposition and the West have accused President Bashar Al-Assad's forces of using chemical weapons on August 21 in a Damascus suburb, a charge denied by the government.
US Secretary of State John Kerry has said blood and hair samples collected from the chemical attack site in Syria have "tested positive for signatures of sarin gas".
He pushed for a military strike against the Assad regime over its alleged use of the deadly weapon.
Meanwhile, two Syrian Government officials have been observing the UN process, as per Ban's guidelines for the procedure, and in strictly in adherence with the established standards for verification set up by the OPCW.
Once analysis of the samples is completed, a report will be given to Ban who will share the results with all Member States and the Security Council.
Ban has been in close contact with the five permanent UN members - China, France, Russia, the UK and the US. He spoke today with French Foreign Minister Laurent Fabius.
Ban is due to brief the 10 non-permanent members of the Security Council on the latest developments "in days to come", possibly tomorrow, his spokesperson said.