By Daisuke Wakabayashi 

Strong sales of Apple Inc.'s new iPhones are pushing the company close to rival Samsung Electronics Co. as the world's top seller of smartphones.

Samsung overtook Apple as the biggest smartphone maker in the third quarter of 2011, according to research firm Canalys. Since then, Samsung has maintained its lead--in shipments if not profits--by offering a wide range of phones. But Samsung's share has been falling, hurt by lackluster sales of its flagship models and the rise of homegrown brands in fast-growing emerging markets. In the third quarter, Samsung shipped about 78 million smartphones, about 25% share of the global market, down from 34% a year earlier, Canalys said.

Enter Apple's new bigger-screen iPhone 6 and iPhone 6 Plus, which went on sale in September. Analysts polled by Fortune forecast that Apple sold 66.5 million iPhones in the quarter ended Dec. 27, up 30% from a year earlier. Some analysts expect iPhone sales to eclipse 70 million units in the quarter.

"It's going to be closer than it's ever been since Samsung took the lead, " said Chris Jones, principal analyst at Canalys.

Apple is expected to disclose iPhone sales Tuesday with quarterly financial results that are expected to include its most profitable quarter ever. Analysts are forecasting Apple to post revenue of $67.5 billion, up 17% from a year earlier, net income of $15.3 billion and earnings per share of $2.58, according to Thomson Reuters. Samsung reports its results on Thursday.

Apple and Samsung declined to comment.

Apple is benefiting from pent-up demand from consumers who waited for iPhones with bigger displays, which proved popular for Samsung and other makers of phones running Google Inc.'s Android software.

Earlier this month, Kantar Worldpanel ComTech said Apple gained share against Android devices in the U.S., Germany, Great Britain, Australia and Spain for the three months ended November. In China, the world's biggest smartphone market, Apple's share increased but its growth was outpaced by Android.

To be sure, Apple's fiscal first quarter is typically its biggest for sales. It coincides with the holiday shopping season and usually follows a new iPhone release. Sales then fall in the following three months--by 14% last year.

Canalys' Mr. Jones said Samsung devices are struggling to stand out from a glut of other Android devices. It's also losing ground to local players in emerging markets, such as Xiaomi Inc. in China and Micromax Informatics Ltd. in India. Apple has weathered the competition better because of its appeal among high-end consumers.

Since 2013 when Samsung's market share lead peaked, Apple also has struck deals with new carriers including China Mobile Ltd. and NTT DoCoMo Inc., the largest carriers in China and Japan, respectively.

Apple isn't only selling more iPhones than ever, it's also selling more expensive phones. The iPhone 6 Plus costs $100 more than Apple's previous high-end model. Plus, Apple is also enticing consumers to upgrade to more expensive models with greater memory.

In the past, Apple offered its latest iPhones with 16 gigabytes, 32 gigabytes, or 64 gigabytes of memory. Each increase added $100 to the price.

With the iPhone 6 and 6 Plus, Apple kept the same pricing model, but offers 16 gigabytes, 64 gigabytes or 128 gigabytes of memory. That has made it more attractive to upgrade, because of the bigger difference in storage between the base model and the larger-capacity versions.

The iPhone 6 Plus and memory upgrades are expected to have increased the average selling price of iPhones by 5% from a year earlier, Morgan Stanley analyst Katy Huberty wrote in a report last week.

Write to Daisuke Wakabayashi at Daisuke.Wakabayashi@wsj.com

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