Samsung smartphone sales are tipped to grow 35% - from 215 million last year to 290 million in 2013 - according to market researcher Strategy Analytics.
Meanwhile Apple's smartphone sales are forecast to reach 180 million this year, up 33% from last year.
This will give the South Korean company a 33% share of the 2013 smartphone market, up from last year's estimated 31%, while Apple's share will rise by 1% to 21%.
According to Strategy Analytics, Apple may respond by launching a smaller and cheaper smartphone - the iPhone Mini.
However, it is not expected to be available before 2014.
"We expect Samsung to slightly extend its lead over Apple this year because of its larger multi-tier product portfolio," Strategy Analytics executive director Neil Mawston said.
Reports suggest Samsung may launch the Galaxy S IV - a new version of its flagship smartphone - in April (Paris: FR0004037125 - news) , and the Galaxy Note III phablet, plus a series of other new smartphones over the course of the year.
"Samsung plays in more segments and this should enable it to capture more volume than Apple (assuming Apple does not launch an 'iPhone Mini' this year)," Mr Mawston added.
The rivals - which dominate the global mobile device market - have been locked in legal disputes around the world over design and technology.
Last month, Apple lost its bid to ban the sale of several Samsung smartphone models in the US.
Shortly afterwards, Samsung announced it was dropping legal action seeking to ban the sale of Apple products in Europe.
In August 2012, Apple was awarded $1.05bn (£655m) in damages after jurors found Samsung had illegally copied critical features of the iPhone and iPad.
A further copyright court case involving the companies over newer products is set to come to trial in the US in 2014.
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