SIMI VALLEY, Calif. — Amazon's decision to protest the Pentagon's cloud computing contract hasn't delayed Microsoft from working on the colossal Joint Enterprise Defense Infrastructure, or JEDI, deal.

"We were working every day before we won that contract to make the product better," Microsoft President Brad Smith told CNBC's Morgan Brennan in an exclusive interview on the sidelines at the Reagan National Defense Forum in Simi Valley, California. "We have if anything been moving even faster since that contract was awarded," he added.

The JEDI contract, which could be worth up to $10 billion for services rendered over as many as 10 years, was awarded to Microsoft on October 25. Last month, Amazon filed a notice in the U.S. Court of Federal Claims indicating a plan to protest the Pentagon's decision to award Microsoft the multibillion-dollar cloud contract.

"Numerous aspects of the JEDI evaluation process contained clear deficiencies, errors, and unmistakable bias — and it's important that these matters be examined and rectified," Amazon told CNBC in an email.

Amazon's AWS chief Andy Jassy told CNBC's Jon Fortt in an exclusive interview that the cloud contracting was not adjudicated fairly.

"You know, there was significant political interference here," Jassy explained of the JEDI award.

"When you have a sitting president who's willing to be very vocal that they dislike a company and the CEO of that company, it makes it difficult for government agencies, including the DoD to make objective decisions without fear of reprisal. And I think that's dangerous and risky for our country," he added.

The billionaire executive has been a constant source of frustration for the president. Bezos owns The Washington Post, which President Donald Trump regularly criticizes for its coverage of his administration. Trump also has gone after Amazon repeatedly for, as he claims, not paying its fair share of taxes and ripping off the U.S. Post Office.

Trump said in July that companies conveyed that the specifications of the JEDI cloud contract favored Amazon.

"I never had something where more people are complaining," Trump said in July at the White House, adding that he was seriously considering looking at the Pentagon contract. "Some of the greatest companies in the world are complaining about it," he added, naming Microsoft, Oracle and IBM.