Revenue was also at an all-time high of $75.9bn (£52.9bn) – though lower than forecast by analysts.
Mr Cook said: “Our team delivered Apple’s biggest quarter ever, thanks to the world’s most innovative products and all-time record sales of iPhone, Apple Watch and Apple TV.”
But the California-based firm also confirmed rumours it is expecting its revenue for the next quarter to decline.
It suggested revenue could be between $50bn and $53bn (£34.8bn and £36.9bn) – down from $58bn (£40.4bn) the same time last year.
It would be the first fall in revenue for Apple in 13 years.
Finance director Luca Maestri attributed Apple’s relatively lacklustre revenue to the strength of the US dollar, which he said knocked about $5bn (£3.5bn) off the total figure.
He also said Apple was beginning to see “signs of economic softness” in China, particularly Hong Kong.
For the last quarter, revenue in “Greater China” was up 14%, but weaker in the Americas, its biggest market, and Japan.
One retail expert said Apple must come up with “revolutionary products” this year if it is to avoid further damage to its growth.
Neil Saunders, chief executive of retail experts Conlumino, said: “While Apple engineers may be excited about shaving a millimetre off the depth of a phone, such technicalities are far less appealing to everyday users.
“The fact remains that 2016 is year when Apple needs to come up with revolutionary rather than evolutionary product. If it fails to do so, its growth is likely to be diminished still further.”
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