Sarah Tew/CNET

Apple's iPhone 5S and iPhone 5 both outsold Samsung's Galaxy S4 worldwide in October, says market researcher Counterpoint.

In its latest Market Pulse report released Thursday, Counterpoint said that the iPhone 5S retained its top spot for global smartphone sales in spite of supply shortages that forced customers to wait to snag the phone. As 5S supply has ramped up, the research firm expects Apple to meet even stronger demand for November and December.

The iPhone 5 took home second place in Counterpoint's rankings, leaving the Galaxy S4 in third. The iPhone 5C was No. 4, followed by Samsung's Galaxy Note 3, Galaxy S3, and Galaxy S4 Mini.

Counterpoint Research

Apple fared well across the world but most notably in China where its market share surged to 12 percent in October from just 3 percent in September, transforming it into the country's third largest smartphone vendor. A deal with China Mobile, which reportedly has already been reached, stands to drive up Apple's share among Chinese consumers even further.

"With a China Mobile deal on the horizon, Apple's iPhone 5S at all three [Chinese] carriers will for sure ignite a 'price war' boosting the overall iPhone 5S sales in China," Counterpoint analyst Tom Kang said in a statement. "This might allow Apple to even reach the No. 1 smartphone player in December or January in China."

Counterpoint's monthly Market Pulse report culls its sales data from surveys of major retailers and distributors across 33 countries.