Google’s Android operating system continues to gain momentum in the U.S. smartphone market, despite stiff competition from Apple’s iPhone.

Sales of Android-based smartphones accounted for almost 44% of U.S. smartphone sales during the third quarter, according to research firm Canalys, up from 34% in the prior quarter. With new Android phones, such as Motorola’s  Droid Pro and the Verizon Fascinate swarming onto the market, Google’s mobile OS is going from strength to strength.

Apple also enjoyed a strong quarter. The tech giant usurped Research In Motion as the top individual vendor. The iPhone maker accounted for 26.2% of the U.S. market, up from 21.7% in the prior quarter. RIM’s share dropped from 32.1% in the second quarter to 24.2% in the third quarter, despite the recent launch of the Blackberry Torch.

Google’s operating system is enjoying phenomenal growth in overseas markets, with Canalys reporting that 20 million Android units were shipped globally in the third quarter, up from 1.4 million in the same period last year.

"With Samsung, HTC, Motorola, and Sony Ericsson all delivering large numbers of Android devices, and with focused efforts from many other vendors, such as LG, Huawei and Acer yielding promising volumes, the platform continues to gather momentum around the world," explained Pete Cunningham, a senior analyst at Canalys, in a statement. "Android has been well received by the market, and in some geographies it is becoming a sought-after consumer brand."

Android sales made up a quarter of the worldwide smartphone market, according to Canalys. Nokia remains the most popular global smartphone vendor, with 33% of the market, although this is down from 38% in the prior quarter. Apple clinched 17% of the worldwide smartphone market in the third quarter, up from 13% in the prior quarter. RIM held its 15% share.

Last week tech research firm IDC reported that Apple is now the fourth largest vendor of mobile phones in the world, behind Nokia, Samsung and LG Electronics. IDC’s research, which includes both smartphones and traditional cellphones, cited Apple’s global rollout of the iPhone 4 as a key catalyst, but noted that RIM posted a record number of unit shipments during the third quarter.

Apple shares rose $4.28, or 1.42%, to $305.26 on Monday, outpacing the Nasdaq, which gained 0.98%. RIM enjoyed a more modest gain, climbing 2 cents, or 0.04%, to $56.94.