Samsung are slowly strengthening their market share in the smartphone industry, closing the gap to within 10% of Apple's iPhone.

The South Korean company saw a dramatic growth during the fourth quarter of 2012, but Apple continues to lead with 39% of smartphone sales, compared to Samsung's 30%.

Research company The NPD Group the rivals are continuing to run away from all the other smartphone makers accounting for nearly 70% of all sales during the period.

“Even taking into account the tremendous sales growth of the Galaxy III and other Samsung smartphones, the iPhone is still king of the U.S.-market hill,” says Stephen Baker, vice president of industry analysis, The NPD Group.

“In addition to strong U.S. sales of iPhone 5, Apple has been bolstered by strong and continued demand for older, less-expensive iPhone models.

Market share:

Apple 39% Samsung 30% Motorola 7% HTC 6% LG 6%

Based on the latest information from NPD, the top-selling mobile phones in the U.S. were as follows:

1 iPhone 5 2 Samsung Galaxy S III 3 iPhone 4S 4 iPhone 4 5 Samsung Galaxy S II

“While smartphone sales continued on their torrid pace in the fourth quarter, the seeds of change are evident in the sales numbers,” Baker says.

“With of the vast majority of all phone sales now smartphones, and with the largest unit-sales growth within smartphones occurring in the pre-paid segment, today's product pricing and channel models will need to adapt to accommodate this new reality.