"For sure we did not conduct any operation inside (the) city," Brigadier General Ahmed al-Assiri, the coalition spokesman, told AFP.
The area, a UNESCO World Heritage site, has been inhabited for 2,500 years and Assiri said "we know that those sites are very important."
He said rebels may have been hiding weapons or ammunition in the area.
"Several days before they had an explosion in one of their storage" areas, he said of the Huthi rebels. "So it could be one of these."
There were conflicting statements from residents about whether rebels had occupied one of the houses.
The Arab-led coalition began bombing the Iran-backed rebels and their allies in late March in an attempt to halt their expansion in Yemen.
It has defended suggestions from rights activists and the United Nations that its bombing has been "indiscriminate."
Assiri said coalition pilots do not strike civilian areas even if anti-aircraft fire is directed at them.
"We just tell our pilots to avoid the positions, to avoid the firing," he said.
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