The UN chief told reporters he takes seriously a recent US intelligence report which indicated Syria has twice used chemical weapons and said "a credible and comprehensive inquiry" requires access to all sites where allegations have been made.
Syria wants any investigation limited to an incident near Aleppo in March, but Ban wants a broader investigation, including a December incident in Homs.
Ban made his appeal for access standing beside Swedish chemical weapons expert Ake Sellstrom, a former UN chemical weapons inspector in Iraq who heads the team, before they met privately. He praised Sellstrom and his team for their "integrity and independence and professionalism."
UN spokesman Martin Nesirky said later that the secretary-general and Sellstrom discussed the steps that have been taken so far in gathering information from a range of sources. He said they agreed that there is no substitute for an on-site investigation to determine if chemical weapons have been used.
Ban stressed earlier to reporters that "on-site activities are essential if the United Nations is to be able to establish the facts and clear up all the doubts surrounding this issue."
He noted that April 29 is the Day of Remembrance for All Victims of Chemical Warfare.
"As we address these allegations," Ban said, "I encourage all involved to uphold their responsibilities in enabling us to properly police these heinous weapons of massive destruction."
In a message marking the day, the secretary-general said the allegations "of the use of these indiscriminate and morally repugnant weapons in Syria serve as a reminder of the continuing vital importance of the Chemical Weapons Convention."
The convention prohibits the development, production, acquisition, stockpiling, retention, transfer or use of chemical weapons by the 188 states that have ratified it. Ban said in the past year, the total of declared chemical warfare agents that have been verifiably destroyed has risen from nearly 75 percent to close to 80 percent.
But the secretary-general said "the threat of chemical weapons persist," noting that eight countries have not ratified the convention - Syria, North Korea, Angola, Egypt, Somalia, South Sudan, Israel and Myanmar.
"Until the convention is universal and the last stockpiles have been destroyed," he said, "our debt to the victims of chemical warfare will remain unpaid."