"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 told a youth event at U.N. headquarters in New York.
Two suicide car bombers killed 55 people and wounded 372 in Damascus on May 10, state media said, the deadliest attacks in the Syrian capital since an uprising against President Bashar al-Assad began in March 2011.
Damascus has maintained all along that it is facing a "terrorist" conspiracy funded and directed from abroad, not least by resource-rich Gulf monarchies Saudi Arabia and Qatar, which have called for arming the fighters aiming to oust Assad.
Syria earlier this month sent the United Nations the names of 26 foreign nationals it said had been apprehended after coming to fight in Syria. It described 20 of those as members of al Qaeda who had entered the country from Turkey.
There are 257 unarmed U.N. monitors in Syria to observe an unraveling five-week-old truce brokered by U.N.-Arab League peace envoy Kofi Annan.
"The deployment of monitors has some dampening effect, the number of violences has reduced but not enough, not all the violences have stopped," Ban said. "We are trying out best efforts to protect the civilian population."
He said at least 10,000 people had been killed in the Syrian conflict.