The company's earnings were announced amid escalating rhetoric around tariffs between the US and China.
Cook said that Apple products have not so far been directly affected, and that the company is evaluating the latest Trump move now in a public comment phase.
Cook said the number of people using Apple devices is surging, and that promised to keep fuelling the strong growth seen at its streaming music, digital wallet, and App Store.
"Each country can only prosper if the other does", he said.
Apple said in a quarterly filing to the Securities and Exchange Commission, or SEC, that its share count was 4,829,926,000 on July 20, less than the 4,842,917,000 it reported on Tuesday for the end of the June quarter. They expect even bigger, fancier iPhones heading into the holidays.
Shares of Apple are rising, up about 0.4% in early trading Tuesday, ahead of the company's third-quarter earnings report after the closing bell.
Cook also said he wasn't fazed at the maturity of the smartphone market, which IDC said shrank 2 percent 342 million units in the quarter.
One area where the tech was more stagnant was iPhone sales, which were only up 1% on this time previous year - but revenue was 20% higher thanks to the price of the flagship iPhone X.
"The lesson Apples management has learned from the iPhone X, is when you sell a smartphone for more than $1,000 you can sell fewer units and still reap the financial benefits", said analyst Thomas Forte from D.A. Davidson & Co.
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Trump on Monday ultimately issued a statement that said: "Despite our differences on policy and politics, I respect Sen". Trump issued presidential proclamations commemorating the deaths of first lady Barbara Bush and pastor Billy Graham.
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John McCain's old political rivals have been paying tribute to the longtime senator after his death at 81 in Arizona on Saturday. A rare Republican critic of Trump, McCain accused the president of "naivete", "egotism" and of sympathizing with autocrats.
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Cook did offer a bit of a tease about a forthcoming video service that Apple reportedly is developing.
Apple also reported a 37 percent increase, to $3.7 billion, in the division for miscellaneous hardware, including Apple Watch and the HomePod smart speaker.
Apple executives emphasized the recurring nature of much of that revenue, saying the company had reached 300 million subscriptions on its devices, a figure that includes both Apple's own services such as music and third-party subscriptions such as Netflix, where Apple takes a cut of the revenue when it handles the billing.
Many were hanging high hopes on Apple's flagship handset and its climbing average selling price (ASP).
Its net cash stood at $129 billion, according to Moody's analyst Stephen Sohn.
Revenue rose 17 percent to $53.27 billion, also exceeding Street forecasts for $52.37 billion.
Apple forecast revenue of $60 billion to $62 billion for its fiscal fourth quarter, beating the $59.6 billion analysts had expected, according to data from Thomson Reuters I/B/E/S.
That beat the $2.17 per share expected by 10 analysts surveyed by Zacks Investment Research.