Its share of sales was up 1.2 percentage points in the US to 31.3 percent, compared with a 0.6 percentage point decline for Android to a 65 percent marketshare. However, iOS sales in urban China fell 4.4 percentage points to 14.3 percent.
That's one more reason why Apple's next iPhone needs to offer consumers a significant reason to upgrade. Apple is gearing up to launch its iPhone 7 lineup this week, although the company isn't expected to make dramatic design changes.
However, it may drop the headphone jack while introducing waterproofing, a new A10 processor, True Tone display, and a new 265GB option on top of the current largest 128GB variant.
Still, according to the market-research firm, the iPhone 6s was the top-selling smartphone in the US with an 11 percent share of sales in the period, while the ageing iPhone 6 accounted for 4.1 percent. It also believes the iPhone SE contributed to growth in several markets.
Apple also made gains in Europe's five major markets including the UK, Germany, France, Italy, and Spain, as well as in Australia, according to Kantar.
Apple's largest gains were in the UK, where its share of sales increased 5.2 percentage points to 38 percent. Across all five EU markets iOS grew 1.2 percentage points to 18.4 percent, while Android was up 6.1 percentage points to 77 percent.
While Apple has reported falling revenues in nearly every region, its challenges in China were more evident in the Kantar Comtech Worldpanel's figures.
Android reached a record high of 85 percent of smartphone sales in China thanks in part to top-seller Huawei, which accounted for 27.6 percent of sales followed by Xiaomi with 18.5 percent of sales. Apple was in third place with a 14.3 percent share.