iPhone5s, 5c
An employee shows the backside of a new Apple iPhone 5C (right) and iPhone 5S (left) at a Verizon store in Orem, Utah, on Sept. 19, 2013. Reuters/George Frey

As Apple (NASDAQ:AAPL) began selling the new iPhone 5s on Friday, new data based on early interest in both the iPhone 5s and iPhone 5c suggest that the company’s smartphone sales could see a 28 percent jump in the third quarter (Apple’s fiscal Q4) of this year.

Katy Huberty of Morgan Stanley said in a recent note to clients, obtained by Fortune, that Apple could sell 34.5 million iPhones in the third quarter of this year, which would be 28 percent higher than the 26.9 million iPhone units the company sold in the same quarter last year.

Huberty’s estimates are based on web searches through Sept. 15, which covers the Sept. 10 iPhone announcement as well as the beginning of pre-orders of the iPhone 5c on Sept. 13. The data include the U.S., U.K., Germany, France, China and Japan markets, all of which are expected to begin selling the new iPhones this week.

“Our model projects demand for the rest of September assuming demand trends post last week's announcement follow a similar pattern as 2012,” Huberty wrote.

However, according to Huberty, sales of Samsung’s (KRX:005935) Galaxy devices in the third quarter of 2013 could outperform iPhone sales. She forecast that the South Korean tech giant could sell 47 million Galaxy devices, an estimate that is 2 million, or 4.4 percent, more than Wall Street's consensus.

Meanwhile, the Wall Street Journal reported on Thursday that Apple has asked its suppliers to boost production of the gold-colored version of the iPhone 5s by an additional one-third as demand for this particular color-option is increasing.

While shipping estimates for all iPhone 5s models have been pushed back soon after the company began accepting online orders on Friday, supply of the gold-colored version of the handset appears to be scarcest, forcing Apple to push its shipping date farther to sometime in October.

In the U.S., the 16GB iPhone 5s on most carriers costs $199 with a two-year contract, while the 32GB and 64GB versions are priced at $299 and $399 respectively. An unlocked GSM version of the iPhone 5s is also available for $649 (16GB), $749 (32GB), and $849 (64GB).