The case comes a day after UBS agreed to pay $780m in fines to the US government and identify a number of its US clients in a deal to resolve criminal fraud charges stating that the bank assisted rich US citizens to evade taxes.
But US tax authorities said the request, made under a Swiss treaty, may only result in the production of records for about 300 accounts.
According to a UBS document filed with the lawsuit, from mid-2000, secret accounts held about $14.8bn in assets.
Other court documents showed that US citizens had failed to report and pay US income taxes on income earned in secret accounts.
The lawsuit also alleged that UBS helped hundreds of US taxpayers set up dummy offshore companies, to make it easier for them to avoid their reporting obligations under US tax laws.
Doug Shulman, the commissioner of the US Internal Revenue Service (IRS), said, "We are committed to moving forward with the summons enforcement process. This action sends a strong signal to taxpayers hiding their money offshore.
"The IRS will be aggressive in pursuing people who shirk their obligations under the tax law," he said.