The US government wants the information so it can examine how effective filtering software is in protecting children from pornography and other harmful websites.
However, Google has refused on a number of grounds, including that the request was vague and unduly burdensome, and that it would reveal trade secrets and could expose identifying information about its users.
The Department of Justice has now asked a judge to compel it to comply with the subpoena, which was issued in August last year. It says that Google's search rivals MSN, Yahoo! and AOL have already complied.
Nicole Wong, a lawyer for Google, said: "Google is not a party to this lawsuit and their demand for information overreaches. We had lengthy discussions with them to try to resolve this, but were not able to and we intend to resist their motion vigorously."
Separately, it is being predicted that the cost of advertising could fall following Google's acquisition of dMarc, a technology company that allows advertisers to book and run radio ad campaigns automatically.
Google bought the company in a $1.2bn deal this week, and is reported to be aiming to become a one-stop shop for advertisers. There are already fears that the move could spell the end of the media buying industry.
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