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Market tracker IDC says Apple's iPad is pulling ahead of tablets made by rivals Samsung, Amazon and others.
Most rival tablets, such as Amazon's touchscreen Kindle Fire and Samsung's Galaxy Tab, run on Google's Android software.
Apple shipped 17 million iPads during the quarter, up from 11.8 million units in the first three months of this year, and well above its previous record of 15.4 million set in the December quarter of last year (and a contrast to the smartphone market, where iPhone sales fell in the second quarter).
More competition is on the horizon with Google's house-brand Nexus 7, a $US249 seven-inch tablet that, like the Kindle Fire, is tied to US-only video, music and other content services.
ABOVE: June quarter shipments in thousands. Click to enlarge.
However, the Nexus 7's initial launch has been beset by shortages.
A 7 or 8-inch "iPad Mini" will be released later this year, The Wall Street Journal reports. Apple has made no comment.