The company's website showed buyers in United Kingdom, France and Germany would have to wait as much as three weeks to receive orders when the iPhone 5 starts shipping next Friday, the first day of deliveries.
However, AT&T Inc, Verizon Communications Inc and Sprint Nextel Corp -- the three US carriers who will sell the iPhone 5 -- kept showing availability for delivery next Friday.
The new model would also be available in Apple's stores next Friday for walk-in purchase. Retailers like Wal-Mart Stores Inc and Best Buy Co are also taking preorders for the new iPhone at their stores.
"When you do a pre-order, the last thing you want to do is upset customers, so obviously they are overwhelmed with the demand. No one wants to sell out in an hour."
Apple shares rose 2 percent at mid-day to $696.68 in heavy trading on the Nasdaq. The shares earlier touched an all-time high of $696.98.
Apple began taking orders for the iPhone 5 at midnight Pacific Time (0700 GMT) on Friday, with shipments set to begin on Sept 21. The smartphone is being rolled out in phases and will be sold in 100 countries by the end of the year.
It is not unusual for Apple products to sell out the first day. Orders for the previous iPhone 4S, the last product the company introduced before the death of co-founder Steve Jobs, surpassed 1 million in the first 24 hours, beating Apple's previous one-day record of 600,000 sales for the iPhone 4.
Analysts have expressed surprise at how quickly Apple planned to roll out the new model around the world, saying this was the fastest rollout of the phone since it launched in 2007. On average, Wall Street analysts are forecasting that Apple may sell well over 42 million units by the end of the year.
But some analysts said the early sell-out may also point to a potential supply crunch.
"We believe the fast sell out indicates both high levels of demand and constrained supply," said Shannon Cross, analyst with Cross Research, an independent research house.
"However, given that the company announced an aggressive rollout schedule, we assume management's plan includes a rapid increase in production," Cross said.
The Japanese company, which is the midst of negotiating a deal with Apple's largest contract manufacturer Hon Hai to buy a stake in the struggling company, has fallen behind schedule on production of screens for Apple's latest iPhone, a source had told Reuters in late August.
The source, who is familiar with Sharp's production operations, did not give an indication of how far behind the output had fallen.