To export items search results as xlsx, us command core/export_file:

svc=core/export_file&params={"spec":{
				"itemsType":<text>,
				"propName":<text>,
				"propValueMask":<text>,
				"sortType":<text>
			    },
			    "force":<uint>,
			    "flags":<long> /* columns flags */ 
}

 Description of other params you can see on page Search items by property

Returns .xlsx file.