Though he did not blame the regime directly, Ban said UN experts will confirm in a report released next week that chemical weapons were used in an attack near Damascus that left hundreds dead.
Assad has vowed to relinquish his chemical arms, after the alleged attack prompted threats of US-led military strikes.
US Secretary of State John Kerry and his Russian counterpart Sergei Lavrov were holding a second day of talks in Geneva Friday to hammer out the details of a Russian plan that emerged this week.
The last-minute Russian initiative caused US President Barack Obama to back away from planned military strikes in response to the chemical attack, which Washington blames on the regime and says killed about 1,400 people.
At the United Nations, Ban lashed out at Assad and said the UN inspectors' report would provide "overwhelming" confirmation that chemical weapons were used.
He said the Syrian leader had "carried out many crimes against humanity" and insisted there had to be "accountability" once Syria's civil war is over.
In Geneva, Washington and Moscow said they hoped the chemical weapons talks would open the door to wider efforts to end Syria's conflict, which has claimed more than 110,000 lives since March 2011.
A spokeswoman for Lavrov said talks were ongoing on Friday evening. "Maybe they will finalise something this evening, maybe the negotiations will continue through the night... The work is continuing."
In any case, Kerry said he would meet Lavrov again later this month -- probably around September 28 -- to try to set a date for a long-delayed peace conference.
He said Washington and Moscow were "working hard to find common ground" to get peace talks going in Geneva that would bring together Assad's regime and the opposition.
Much of the way forward "will obviously depend on the capacity to have success here in the next day, hours, days, on the subject of the chemical weapons," Kerry told reporters after meeting with Lavrov and the UN-Arab League envoy to Syria, Lakhdar Brahimi.
Lavrov said he also hoped a "basically abandoned" peace plan first agreed in Geneva in June last year would be revived.
"We agreed to meet in New York in the margins of the (UN) General Assembly and see where we are, and what the Syrian parties think about it and do about it," Lavrov said.
France said Kerry, French Foreign Minister Laurent Fabius and British Foreign Secretary William Hague would hold further talks on Syria in Paris on Monday.
Kerry will also meet Saudi Foreign Minister Saud al-Faisal while in Paris, the US State Department said.
Assad confirmed for the first time Thursday that Syria planned to relinquish its chemical arms, and Russian President Vladimir Putin urged the global community to take him seriously.
"This confirms the serious intentions of our partners to go along this path," Putin said at a security summit in Kyrgyzstan.
Syria on Thursday filed documents at the United Nations seeking to join the international convention banning chemical weapons and said it now considers itself a full member.
A UN spokesman said Friday the organisation has asked Syria for more information about its application, but he declined to say what was missing from the documents filed.
Washington has warned the regime that further steps will be needed before military action would be off the table.
France -- Washington's main backer on military strikes -- also said Friday that Syria had not yet not done enough, calling for a binding UN Security Council resolution that would authorise force if Assad does not give up his arsenal.
"The Syrian regime's announcements are certainly very useful but also certainly insufficient," French foreign ministry spokesman Philippe Lalliot said.
Fuelling concerns about Assad's sincerity, reports emerged Friday that a secret Syrian military unit was scattering the chemical weapons stockpile around the country.
The unit was given responsibility to shift the arsenal of poison gases and munitions to different locations across Syria, the Wall Street Journal reported, citing US and Middle Eastern officials.
Russia has not revealed many details of its plan, but Russian media report that it calls for a four-step process for the weapons handover.
Reports say the plan calls for Damascus to join the Organisation for the Prohibition of Chemical Weapons (OPCW), declare the locations of its chemical arms, allow OPCW inspectors access and finally arrange for destruction of the arsenal.
A spokesman for the Hague-based OPCW said it will meet next week to examine Syria's request.
Syria's opposition National Coalition also said it was "deeply sceptical" of the government's move and urged a tough UN resolution to enforce the measure.
"It is vital the threat of force stays on the table. For a (UN Security Council) resolution to be anything other than a get-out-of-jail-free card for the regime, it must be enforceable under Chapter 7," allowing military action, it said in a statement.
The French presidency said meanwhile that France, Saudi Arabia, the United Arab Emirates and Jordan had agreed to give more help to the Syrian opposition in its battle against Assad.
After a meeting in Paris, French President Francois Hollande and foreign ministers from the three countries "agreed on the need to strengthen international support for the democratic opposition to allow it to face attacks by the regime," Hollande's office said in a statement.