Ban said President Bashar al-Assad has still not implemented a peace plan agreed with UN-Arab League envoy Kofi Annan.
"Very alarmingly and surprisingly, a few days ago, there was a huge serious massive terrorist attack. I believe that there must be Al-Qaeda behind it. This has created again very serious problems," Ban said at a youth event at the UN headquarters.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Suicide attackers detonated huge bombs in Damascus on May 10, killing at least 55 people and wounding nearly 400.
Syria has accused Al-Qaeda of orchestrating attacks in the country in recent weeks, adding to the strife caused by the uprising against Assad.
"More than 9,000, at least, maybe 10,000 people have been killed during the last 15 months. It has reached an intolerable situation now," Ban said.
US and Russian officials have also said they believe Al-Qaeda and other violent militants are now operating in the country.
This month, Syria sent the United Nations the names of 26 mainly Tunisian and Libyan nationals it said had been detained. About 20 had confessed they were members of Al-Qaeda, according to a letter sent with the list.
Ban also highlighted two bomb attacks against convoys of UN ceasefire monitors in Syria.
The UN secretary-general said that apart from the deployment of the monitors, no part of the six-point Annan plan has been implemented.
"We are trying our best efforts to protect the civilian population," Ban said.
The deployment of the monitors has had a "dampening effect" and reduced the violence, "but not enough, not all the violence has stopped. So we will continue, as much as we can, to protect the civilian population," he added.
