Amazon is backing down from a fight with one its biggest publishing partners. Last Thursday, Macmillan CEO John Sargent gave Amazon an ultimatum on pricing for its eBook titles.

In an open letter printed in a special Saturday issue of Publishers Marketplace, Sargent said he told Amazon that the publisher was going with a fixed agency-wide pricing model that would apply to all of its eBooks going forward. Under the agency model, Macmillan would sell the digital editions of its books to consumers through its retailers. The retailers would take a 30 percent commission.

Macmillan’s plan would price the digital editions of most adult trade books in a price range from $14.99 to $5.99. At first release, concurrent with a hardcover, most titles would be priced between $14.99 and $12.99. Ebooks will almost always appear on the same day as the physical edition, with dynamic pricing over time.

“The agency model would allow Amazon to make more money selling our books, not less. We would make less money in our dealings with Amazon under the new model,” Sargent wrote.

Amazon, which until now has stuck with its price of $9.99 for most new releases, was not impressed, and promptly pulled all of Macmillan’s titles from its virtual shelves on Friday. However, the disappearance of Macmillan’s titles from Amazon didn’t last long. All of Macmillan’s titles were back online by this morning.

In a statement addressed to its customers, Amazon explained its decision to accept Macmillan’s demands.

“We want you to know that ultimately, however, we will have to capitulate and accept Macmillan’s terms because Macmillan has a monopoly over their own titles, and we will want to offer them to you even at prices we believe are needlessly high for e-book. Amazon customers will at that point decide for themselves whether they believe it’s reasonable to pay $14.99 for a bestselling e-book,” the statement read.

The dispute comes as Apple is set to shake up the eReader market with the iPad, which will come in versions that run on Wi-Fi and on Wi-Fi and 3G provided by AT&T. Apple has for months been jockeying for agreements with content partners in an effort to provide a wide selection of everything from movies to eBooks for its new device.

Apple’s CEO, Steve Jobs, took a swipe at Amazon following the iPad unveiling in San Francisco last week.  Jobs told Walt Mossberg of The Wall Street Journal‘s All Things Digital blog, in a brief interview posted online, that eBook prices will eventually be the same across the board.

“Publishers are actually withholding books from Amazon because they’re not happy,” Jobs told Mossberg.