By Daniel Stacey and Ross Kelly 

SYDNEY-- Apple Inc. began sales of its newest iPhones Friday with consumers in Australia becoming the first globally to get their hands on them.

With the appeal of a bigger screen, veterans of prior launches said the queues were the longest outside Sydney's Apple store, highlighting strong initial demand.

"Apple customers wanted bigger screens and now they have finally done it, " said Shane Gray, who had lined up for 15 hours on the sidewalk with his wife and young son.

"You don't have to pinch and zoom with emails and Web pages."

Mr. Gray, who had made a similar pilgrimage to the city-center store from southwest Sydney for the past five iPhone launches, said he had been flirting with the idea of switching smartphones after becoming frustrated with Apple's reluctance to provide a bigger screen.

Apple's 4.7-inch iPhone 6 and 5.5-inch iPhone 6 Plus are bigger than the current four-inch display of the iPhone 5S. They will compete with makers of Android phones, such as Samsung Electronics Co. whose flagship Galaxy S5 has a 5.1-inch screen.

The screen upgrade, along with better battery life, a faster processor, and an improved camera, is expected to drive strong demand for the new phones. In an interview last week, Apple Chief Executive Tim Cook said he expects the "mother of all upgrades" from consumers rushing to snap up the new iPhones.

Mr. Gray and his family were among 1,300 people Apple staff estimated were waiting in line and that they estimated to be the largest since the store opened six years ago. Inside the store, around 200 Apple staff dressed in blue T-shirts and jeans on the balcony clapped as the clock ticked down for the first iPhones to go on sale.

First in line was 22-year-old Salvatore Gerace, who works for social commerce platform Alphatise and wanted to snap up the first pair of iPhones as part of a publicity stunt. Mr. Gerace and colleagues had worked in rotating shifts over 10 days to maintain their place at the head of the line.

"We're here to give away the first two iPhones we get in the world for free," he said.

Earlier this week, Apple said it received more than four million orders for its two new iPhones in the first 24 hours after it started accepting preorders on Sept. 12--more than it had set aside for preorders.

Apple's main manufacturing supplier, Hon Hai Precision Industry Co., has employed more than 200,000 people on about 100 production lines exclusively for the new iPhones around the clock at a Chinese manufacturing site, according to people familiar with the matter.

With its larger phones, Apple is hoping to attract and retain high-end consumers, who are favoring larger displays.

Research firm Canalys says that in recent months, nearly all smartphones selling for more than $400 and running on Google Inc.'s Android operating system come equipped with a display larger than 5 inches.

Apple has raised the base price for its most-expensive model by $100. The iPhone 6 starts at $649 without contract--the same price that Apple charged for the iPhone 5S when it introduced that phone a year ago. For the larger iPhone 6 Plus, Apple is charging $749 without contract, making it the most expensive iPhone that the company has ever sold.

The higher price hasn't done much to diminish demand. The waiting time for the iPhone 6 Plus is longer, at three-to-four weeks, while customers can get an iPhone 6 within seven to 10 business days, according to the company's online store in the U.S. Apple said it has set aside supplies for customers purchasing the phones in stores on Friday.

One worrying sign, however, for the new iPhones is that Apple hasn't announced a launch date for the Chinese market. Last year, Apple introduced its new iPhones in the Chinese market at the same time that it launched globally. The Chinese government hasn't approved the phones for sale yet, but it wasn't immediately clear the real reason for the holdup.

Angela Ahrendts, Apple's senior vice president of retail and online stores, welcomed the first customers into the company's flagship Australian store on George Street in Sydney. The former chief executive of luxury products maker Burberry Group PLC had traveled Down Under from Apple's headquarters in Cupertino, Calif.

David Rahimi and his girlfriend, Jasmine Juan, were the first to exit the store clutching new iPhones. The couple had traveled from Orange County, Calif., after becoming part of a small group of Apple customers able to reserve the new phones online.

Mr. Rahimi, who reviews cellphones for PhoneBuff.com in his role as editor in chief, bought the 5.5-inch iPhone 6 Plus for himself while Ms. Juan bought the 4.7 inch iPhone. The couple also bought two more 4.7 inch phones.

"Finally Apple has a bigger screen," Mr. Rahimi said. "It's something I have been looking forward to."

Mr. Rahimi typically uses Samsung's Galaxy Note, but said the 5.5-inch iPhone 6 Plus will likely become his primary phone now.

Daisuke Wakabayashi and Lorraine Luk contributed to this article.

Write to Ross Kelly at ross.kelly@wsj.com

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