The court document cites the decision by the Department of the Interior (DoI) to exclude Google's Apps for Government services from bidding on a contract to consolidate 13 platforms into one cloud system. The five-year contract is for around 88,000 users, and is worth $59m (£36.7m).
The DoI claimed that "based on the risk assessments and market research" Microsoft had "the only commercial product that satisfies every requirement identified by the department".
Google said that the company had repeatedly expressed an interest in bidding for the contract, but was originally turned down because its Apps service did not meet DoI security requirements.
Google explained that the firm held frequent meetings to show that it met the government requirements, but was told that the decision on a new messaging system had already been made.
The search firm was also told that it did not meet Federal Information Security Management Act standards, although it is now certified to this level.
Last week the Government Accountability Office dismissed Google's complaints, and that of its reseller Onix, on the ground that Google "was not an interested party". The company has responded with the lawsuit.
Cloud service vendors are increasingly courting government business as the US and UK governments have indicated that they want government services to be run at lower cost.
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