Some Verizon Wireless customers complained they were unable to buy its iPhone online, but the phone company said sales were mostly running smoothly on its first day of Internet orders for the long-awaited phone.

The No. 1 U.S. mobile service started taking online orders for its Apple Inc iPhone at 3 a.m. EST on Thursday, a week before it is due to hit its store shelves. Verizon Wireless had said it was preparing for heavy demand.

Spokeswoman Brenda Raney said the company was pleased with how the online system had performed and that the majority of customers have been able to process their orders with no problems. However, this was not the case for everybody.

We are aware that some customers have received error messages and we are working through the issues with the individuals to ensure they get their order placed, Raney said.

Verizon's launch of online sales ended AT&T Inc's more than three-years' hold on U.S. operator distribution of the popular device. Some analysts say Verizon Wireless could sell as many as 13 million iPhones this year.

When AT&T and Apple launched pre-orders of the iPhone 4 in June last year heavy demand had caused technical problems on both companies' websites.

Verizon Wireless is a venture of Verizon Communications and Vodafone Group Plc.

(Reporting by Sinead Carew and Jonathan Oatis; editing by Dave Zimmerman)