Chairman Lee Kun-hee's said his company flogged over 20,000 Galaxy smartphones an hour between in January and March.
After selling 44.5 million smartphones, Samsung has a 30.6 percent share of the high-end market. Apple's sales of 35.1 million iPhones gave it a 24.1 percent share.
Neil Mawston, an analyst at Strategy Analytics told Reuters that the battle of the smartphone was becoming a two horse race.
Other analysts say that they do not expect things to change much this year or next.
Samsung will launch in London of a third generation of the flagship Galaxy S, hoping to boost sales ahead of the summer Olympics, where the company is among the leading sponsors.
The Galaxy S 3 will be powered by Samsung's quad-core microprocessor, and most analysts think it will do extremely well.
Samsung also cleaned Apple's clock in the China smartphone market where it has more than 30 percent share of a market.
According to Samsung's quarterly handset division profits increased to $3.8 billion, accounting for 73 per cent of total profit. They are on operating margins jumped to 18.4 percent from 12 percent in the preceding quarter on strong sales of the Galaxy S and the Note phone/tablet.
Samsung has also overtaken Nokia as the global mobile phone leader and its January-March operating profit nearly doubled.
While it would be hard to see anything negative in these figures there are some analysts who believe that Samsung's handset earnings growth may slow later this year when Jobs' Mob releases its iPhone 5. However they also said that about the somewhat disappointing iPhone 4S which failed to stop Samsung's rise to glory.