In a report to the UN Security Council, he said it would take 100 foreign experts to complete "an operation the likes of which, quite simply, has never been tried before."
The Organisation for the Prohibition of Chemical Weapons said it would send a second team to Damascus to bolster an existing UN-OPCW group on the ground.
"That will augment the advance team of OPCW experts, who have been in Syria since 1 October conducting verification and destruction activities," it said, without providing details.
OPCW Director General Ahmet Uzumcu said the process of destroying Syria's chemical arsenal would be "long and difficult" but welcomed a "constructive beginning" to the operation.
The inspectors have until mid-2014 to verify and destroy the arsenal under the terms of a UN Security Council resolution that enshrines a US-Russian deal.
The deal averted threatened US military action in response to August 21 sarin gas attacks outside Damascus in which hundreds of people died.
Meanwhile, Russian President Vladimir Putin praised Syria's President Bashar al-Assad for his government's cooperation with the inspectors.
"Doubts about whether the Syrian leadership would adequately respond to the decision taken on chemical weapons -- these doubts did not bear out," Russian news agencies quoted Putin as saying.
"The Syrian leadership has very actively joined this work and is acting in a transparent manner, helping international agencies."
Ban: 'Dangerous' work for inspectors
On Monday, Ban warned of the dangers the inspectors face in Syria, where the Observatory says more than 115,000 people have been killed since March 2011.
They would have to work in "dangerous and volatile" conditions, particularly in urban areas such as Damascus, Homs and Aleppo, he warned.
"Heavy artillery, air strikes, mortar barrages and the indiscriminate shelling of civilian areas are commonplace, and battle lines shift quickly."
Syrian television provided a first video of the inspectors at work.
The footage shows several of them in protective gear, including helmets, gloves and, in one instance, a gas mask, inside a building.
Additional footage shows an inspector in a gas mask and gloves appearing to be taking readings from barrels.
Some 19 OPCW arms experts and 16 UN logistics and security personnel are in Syria and have started to destroy weapons production facilities.
Ban recommended the team be increased to about 100 scientists, logistics and security experts who will stay for up to a year.
The mission will have bases in Damascus and Cyprus.
Syria has already made a declaration of its weapons facilities, and the UN resolution set a November 1 deadline for the eradication of production and chemical mixing facilities.
That work started Sunday when the first missile warheads, aerial bombs and mixing and filling equipment were destroyed, according to the UN.
The Security Council resolution threatens "measures" under Chapter VII of the UN Charter if an infringement of the disarmament accord is proved.
Chapter VII allows for possible military action or sanctions.
But US Secretary of State John Kerry has welcomed the progress made so far.
"I think it's extremely significant that yesterday, Sunday, within a week of the resolution being passed, some chemical weapons were being destroyed," he told reporters in Indonesia on Monday.
"I think it's a credit to the Assad regime, frankly. It's a good beginning and we welcome a good beginning."
Meanwhile fighting continued, with Syrian jets firing at rebels in the northwestern province of Idlib a day after they launched a major assault on the Wadi Deif and Hamidiyeh military bases.
In Budapest, Ban called for action over the dire humanitarian situation in Syria.
"The Security Council has... made a strong commitment to relieve the humanitarian situation to reach millions of desperate civilians. Now these commitments must be backed by action," he said.