The world's most valuable public company got a little more expensive on Tuesday, as strong demand for the new iPhone 5 pushed Apple shares above the $700 US a share level for the first time.

Apple shares closed at $701.91 on the Nasdaq early Tuesday, up $2.13 from Monday's finish. That was the first time the shares had passed the $700 level during regular trading. They first broke that level during after hours trading yesterday.

On Monday, Apple announced that orders for its iPhone 5 topped two million in the first 24 hours. 

"This was despite somewhat lukewarm reviews and some claiming it had 'lack of a wow factor,'" Sterne Agee analyst Shaw Wu said in a note to investors. "We continue to believe many underestimate iPhone 5 in that it is a significant update and will drive a powerful product cycle."

Wu estimates that Apple will likely ship 27 million iPhones in the current quarter.

The rally in its stock price puts its value at $656 billion, more than any public company has ever been worth, if one ignores inflation.

The $700 figure is little more than a symbolic moment, and a nice round number for the high-flying tech darling. Indeed, many shares, including Apple rival Google Inc., have traded above that level. But Apple's total market capitalization has left all others in its wake.

Apple shares have almost doubled, up 87 per cent, since Oct. 5, 2011, when Apple founder and CEO Steve Jobs died.

With files from The Associated Press