Pre-orders for Apple's new plastic-backed, brightly colored iPhone 5C have not been "overwhelming," and supply of both that model as well as a more expensive phone has been disappointing, a source at a US wireless carrier told Reuters on Tuesday.

Apple unveiled two iPhone models - the 5C as well as a more expensive 5S - last week, with the eye-catching 5C marking a departure from Apple's focus on purely premium phones.

Apple began taking online orders on Friday for the iPhone 5C, which comes in blue, green, pink, yellow and white and starts in the United States at $99 with a contract. Both phones go on sale in several countries on September 20.

The level of inventory Apple has said it would provide for the 5S and 5C on launch day and in the week after launch is very disappointing, the source said, adding that supply of phones to all carriers appears to be limited.

Pre-orders are "not overwhelming" either, said the source, who refused to be identified because Apple has not disclosed the number of pre-orders for either of its two new smartphones.

The pricier '5S' begins at $199 with a contract and comes in three colors - gray, silver and gold. The phones will mainly be sold through four major US carriers - AT&T, Verizon, Sprint and T-Mobile . Representatives from all four carriers declined to comment.

Apple could not be reached immediately for comment. - Reuters