Stock in the maker of Macs and mobile devices hit $701.44 (around £430) in morning trading Tuesday, up a quarter of a per cent from Monday's price. It is currently at around $700.
This comes just a day after Apple announced that its latest smartphone, the iPhone 5, sold 2 million advance orders in its first 24 hours last Friday (September 14), beating the previous 1m record of the iPhone 4S.
Apple currently has a market capitalisation of around $656 billion (£404 billion), more than any public company has ever been worth, without factoring in inflation.
On Friday (September 21), Apple will start sales of the iPhone 5, its new smartphone featuring a 4-inch screen, faster A6 processor, iOS 6 operating system, improved camera and better battery.
The company is forecast to sell up to 6m handsets over the opening weekend and could shift up to 10m over the first week of sales, which would make the iPhone 5 Apple's most successful ever product.
Due to massive demand for the smartphone, Apple expects that some ordered devices will not be delivered until October.
Apple is expected to enjoy broad success with its iPhone 5 in the third and particularly fourth quarters of 2012, the first signs of which we will see at the company's Q3 earnings call on October 15.
However, Apple is also facing competition from phones running Google Android, the most popular mobile operating system in the world.
Samsung's Galaxy S3 smartphone has already sold more than 20m units since it was launched earlier in the year, while Google's own Motorola Mobility announced a new RAZR i Android phone today, featuring a HD screen and superfast processor.
Another competitor is Microsoft's new Windows Phone 8 platform, which launches next month and has already been announced for various top-end handsets, including the Nokia Lumia 920.