Holder refused requests by the House Oversight and Government Reform Committee to hand over - without preconditions - documents that could explain why the Justice Department initially denied in February 2011 that a risky tactic was used to allow firearms to "walk" from Arizona to Mexico.
Federal agents lost track of many of the guns. The operation identified more than 2,000 illicitly purchased weapons, and about 1,400 of them have yet to be recovered.
The department failed to acknowledge its false statement for 10 months.
"Portentously, the [Justice] Department from the outset actively resisted cooperating fully with the committee's investigation," the lawsuit said.
"Among other things, the department initially declined to produce documents; later produced only very limited numbers of documents in piecemeal fashion; refused to make available to the committee certain witnesses; and limited the committee's questioning of other witnesses who were made available," it said.
The Justice Department previously said it would not bring criminal charges against its boss. Democrats have labeled the civil and criminal contempt citations a political stunt.
In response to the lawsuit, Justice Department spokeswoman Tracy Schmaler said, "We were always willing to work with the committee. Instead, the House and the committee have said they prefer to litigate."
Several lawmakers said this was the first time a cabinet official had been held in contempt.
The lawsuit asked that:
The executive-privilege claim by Obama be declared invalid.
Holder's objection to the House records subpoena be rejected.
The attorney general produce all records related to the Justice Department's incorrect assertion in early 2011 that gun-walking did not take place.
Obama asserted a broad version of executive privilege to keep Justice Department documents secret.
The lawsuit said the documents "would enable the committee (and the American people) to understand how and why the department provided false information to Congress and otherwise obstructed the committee's concededly legitimate investigation."
It challenged the executive-privilege claim on several legal grounds, contending that it was asserted indirectly by the deputy attorney general in a letter to Congress and that the documents did not involve any advice to the president. The department's actions, the suit said, do not involve core constitutional functions of the president.
The battle over congressional subpoenas for documents and testimony arose when Congress looked into whether political motives and White House involvement had prompted the dismissal of U.S. attorneys.
Gun-walking long has been barred by Justice Department policy, but federal agents in Arizona experimented with it in three investigations during the George W. Bush administration before Operation Fast and Furious. The agents in Arizona lost track of several hundred weapons in that operation.