After a brief pause, both men continued to take questions at an event marking Ban's first visit to the Iraqi capital.
An Iraqi security official said the explosion had been caused by a mortar shell fired into the area. There were no initial reports of casualties.
The loud blast sent a column of smoke and dust into the sky near the northern edge of the Green Zone, opposite the Jumhuriyah Bridge in downtown Baghdad in a heavily policed area surrounded by government offices.
Immediately before the explosion, Ban told reporters: "I'm confident that we'll be able to see, in the near future, a more prosperous and secure... and a healthier future of the Iraqi people and government."
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