President Donald Trump speaks with Satya Nadella, Chief Executive Officer of Microsoft, and Jeff Bezos, Chief Executive Officer of Amazon during an American Technology Council roundtable in the State Dinning Room at the White House in Washington, DC on Monday, June 19, 2017.

Lawyers for the federal government asked that a court to allow the Department of Defense (DoD) to reconsider its decision to award a $10 billion cloud services contract to Microsoft that sparked a legal challenge from Amazon Web Services.

In a motion filed with the U.S. Court of Federal Claims on Thursday, lawyers asked for the court to grant the DoD "120 days to reconsider certain aspects of the challenged agency decision." The DoD would use the time to amend its solicitation of proposals and allow "limited" revisions addressing the provider's technical approach to a specific price scenario.

The providers could only adjust the solutions they already proposed, not propose new storage solutions, under the terms requested by the government. The DoD would also reevaluate the providers' "online marketplace offerings" and "reconsider its award decision in response to the other technical challenges presented by AWS."

Microsoft did not oppose the motion, according to the filing, but counsel for AWS told the government it did and planned to file its own motion in response.

Amazon sounded supportive of the motion in a statement to CNBC, but the company plans to respond with its concerns that a review may not address all of the alleged biases and errors it claimed in the original complaint.

In the statement, a spokesperson for Amazon Web Services said, "We are pleased that the DoD has acknowledged 'substantial and legitimate' issues that affected the JEDI award decision, and that corrective action is necessary. We look forward to complete, fair, and effective corrective action that fully insulates the re-evaluation from political influence and corrects the many issues affecting the initial flawed award."

In a statement to CNBC a spokesperson for Microsoft said, "We believe the Department of Defense made the correct decision when they awarded the contract. However, we support their decision to reconsider a small number of factors as it is likely the fastest way to resolve all issues and quickly provide the needed modern technology to people across our armed forces. Throughout this process, we've focused on listening to the needs of the DoD, delivering the best product, and making sure nothing we did delayed the procurement process. We are not going to change this approach now."

A spokesperson for the DoD said in a statement, "While we disagree with the Court's decision, we must address the findings in the Court's Order with the intent of ensuring our warfighters will get this urgent and critically needed technology as quickly and efficiently as possible. As such, the Department determined that the best and most efficient path forward is to conduct a re-evaluation of the proposals in order to address the Court's noted concerns. The Department maintains the JEDI Cloud contract was awarded based upon a fair and unbiased source selection process. The process consisted of a fair evaluation of proposals based solely on the solicitation's stated criteria and the proposals submitted."

The motion comes after a judge temporarily blocked the contract at the request of AWS. In its initial complaint over the government's decision to award the up to 10-year contract to Microsoft late last year, AWS claimed President Donald Trump's repeated criticisms of Amazon and its CEO Jeff Bezos influenced the DoD's decision.

"The question is whether the President of the United States should be allowed to use the budget of DoD to pursue his own personal and political ends," AWS wrote in its earlier complaint. "DoD's substantial and pervasive errors are hard to understand and impossible to assess separate and apart from the President's repeatedly expressed determination to, in the words of the President himself, 'screw Amazon.' Basic justice requires re-evaluation of proposals and a new award decision."

AWS argued the DoD "ignored the plain language of AWS' proposal" and "glossed over wide gaps" between AWS's market leading position in the cloud computing industry and Microsoft's Azure. AWS has sought to depose Trump, Defense Secretary Mark Esper and former Defense Secretary James Mattis in the case.

At the time, a spokesperson for the Pentagon denied any "external influences" on the JEDI award decision.

-CNBC's Annie Palmer and Jim Forkin contributed to this report.

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