The Pentagon awarded the contract to Microsoft in late October, and Amazon said there was "unmistakable bias" on the government's part and it intended to challenge the decision in court.
Esper recused himself from the contract decision because his son had worked for one of the other unsuccessful bidders.
"I am confident that it was conducted freely and fairly without any type of outside influence," Esper said at a news conference in Seoul, South Korea.
Amazon's competitive bid for the "war cloud" project drew criticism from President Donald Trump and its business rivals. The project, formally called the Joint Enterprise Defense Infrastructure, or JEDI, pitted leading tech titans Microsoft, Amazon, Oracle and IBM against one another
In a statement Thursday, Amazon said "numerous aspects" of the bidding process involved "clear deficiencies, errors, and unmistakable bias." It did not elaborate on those allegations but said "it's important that these matters be examined and rectified."
Microsoft did not respond to a request for comment. A Defense Department spokeswoman would only say that the Pentagon won't speculate on potential litigation.
JEDI will store and process vast amounts of classified data, allowing the U.S. military to use artificial intelligence to speed up its war planning and fighting capabilities.
Amazon was long thought to be the front-runner for the contract. Its Amazon Web Services division is far ahead of second-place Microsoft in cloud computing, and Amazon has experience handling highly classified government data.
It survived earlier legal challenges after the Defense Department eliminated Oracle and IBM and whittled the competition to the two Seattle-area tech giants before choosing Microsoft in late October.
The Pentagon was preparing to make its final decision when Trump publicly waded into the fray in July, saying he had heard complaints about the process and that the administration would "take a very long look." He said other companies told him that the contract "wasn't competitively bid." Oracle, in particular, had unsuccessfully argued Pentagon officials unfairly favored Amazon for the winner-take-all contract.
Experts had generally expected Amazon to appeal the award, saying it had little to lose. Steven Schooner, a professor of government procurement law at George Washington University, said Trump's comments were "inappropriate and improvident," but said it would be a challenge for Amazon to prove the White House applied undue pressure in a way that made a difference.
Amazon said it filed its protest in the U.S. Court of Federal Claims, which deals with financial claims against the federal government.
It's not uncommon for losing bidders to file a protest, either with the U.S. Government Accountability Office or in court. Unlike a review by the GAO, Amazon's court filing will enable it to seek documents from the government as evidence for its case.
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