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The audit makes clear that “the overwhelming majority of federal agencies are neither fulfilling the president’s promise of an open and transparent government for the American people, nor complying with the vital reforms to the FOIA process that Congress demanded,” said Senate Judiciary Committee Chairman Patrick J. Leahy, Vermont Democrat, who helped write those laws.

Sen. John Cornyn, Texas Republican and co-author of the 2007 law, said Mr. Obama’s pledge to make his administration “the most open and transparent in history” is falling far short of his goal.

The TRAC study found that the State Department saw the largest percentage increase in FOIA lawsuits — a 111 percent jump from the final two years of Mr. Bush’s presidency to the final two years of Mr. Obama’s first term. Next were the Agriculture Department, a 67 percent increase; the Department of Veterans Affairs, 60 percent; the EPA, 60 percent; Justice, up 50 percent; the Social Security Administration and the Department of Health and Human Services, each up 45 percent; the CIA, up 43 percent; and the Pentagon, up 22 percent.

Among the agencies with fewer FOIA lawsuits under Mr. Obama were the Office of the U.S. Trade Representative, down 67 percent; the U.S. Small Business Administration, also down 67 percent; the U.S. Postal Service, down 57 percent; the Department of Transportation, down 56 percent, and the Merit Systems Protection Board, down 50 percent.

Tom Fitton, president of the public-interest group Judicial Watch, said the administration has a pattern of forcing FOIA requests into court.

“One of the biggest lies of the Obama narrative is the supposed commitment to transparency,” Mr. Fitton said. “It’s far less transparent than the Bush administration. Just to get a response, in terms of the initial request for documents, we have to sue. We have nearly 1,000 Freedom of Information Act requests, and we’re coming up on 100 Freedom of Information lawsuits against the administration. Everybody agrees that the federal government is doing more than ever, but the transparency hasn’t kept up with the increased activity.”