Since last November, a growing number of state attorneys general have been pointing their fingers at Exxon Mobil, investigating whether the energy company’s research about climate change conflicted directly with its public statements on the issue.

But now the accusers are being accused, with a battle being waged over principles of free speech, government overreach and collaboration with activist organizations.

Representative Lamar Smith, Republican of Texas, sent a letter on Wednesday to the New York attorney general, Eric T. Schneiderman, demanding all communications since 2012 between his office and climate change activist organizations.

The attorneys general, Mr. Smith said, are doing the bidding of environmental activists who set out to make pariahs of Exxon Mobil and its industry in pursuit of policies to limit climate change.