* U.S. accuses David Rainey, Kurt Mix of obstruction * 2010 offshore spill largest in U.S. history By Jonathan Stempel June 19 (Reuters) - Federal prosecutors unveiled new criminal indictments on Wednesday against a former BP Plc executive and a former BP engineer charged with obstructing investigations into the April 2010 Gulf of Mexico oil spill. The new indictment of former executive David Rainey adds language suggesting he knew of the congressional probe he was charged with obstructing when he provided false information soon after the spill to members of the House Committee on Energy and Commerce, including about the rate that oil flowed from the ruptured Macondo well. Last month, U.S. District Judge Kurt Engelhardt in New Orleans dismissed a count of obstruction of Congress against Rainey in part because it lacked sufficient detail, which the revised indictment is intended to address. A second count accuses Rainey, a former BP vice president of exploration for the Gulf of Mexico, of lying to investigators in an April 2011 interview about how he calculated the flow rate. The other revised indictment still accuses former BP engineer Kurt Mix of two obstruction counts for allegedly deleting records related to the oil flow rate, but reduces the number of voice mails he allegedly deleted. Lawyers for Rainey and Mix did not immediately respond to requests for comment. Both defendants pleaded not guilty last year and are scheduled to be arraigned under the new indictments on June 25. Rainey's trial is scheduled for Oct. 15 and Mix's trial for Dec. 2, court records show. Two former well site leaders, Robert Kaluza and Donald Vidrine, were also criminally charged and have pleaded not guilty. The explosion of the Deepwater Horizon resulted in 11 deaths and caused the worst offshore oil spill in U.S. history. BP agreed to plead guilty to obstruction of Congress, a felony, as part of a $4.5 billion criminal settlement last November with the U.S. Department of Justice. The cases are U.S. v. Rainey, U.S. District Court, Eastern District of Louisiana, No. 12-cr-00291; and U.S. v. Mix in the same court, No. 12-cr-00171.