The Federal Trade Commission has accused the Justice Department of violating a 43-year-old agreement in an apparent power play to gain jurisdiction over Mobile Corp.'s proposed $8.2 billion takeover of Conoco Inc.

The independent commission said the Justice Department has ignored the traditional guidelines for determining which of the two enforcement agencies will handle the antitrust investigation surrounding the battle for control of Conoco Inc.

In a letter signed by Acting FTC Chairman David Clanton, a Republican, and endorsed by the entire commission, the commission charged that the Justice Department's antitrust division is seeking to use the Conoco case as a means to provide signals to the public about the Reagan administration's merger policy.

Justice Department officials could not be reached for comment.

Conoco, the nation's ninth largest industrial corporation, is the takeover target of E.I. du Pont de Nemours & Co. and Seagram Co. as well as Mobile.

The FTC lost a tense battle with the Justice Department for control of the Du Pont bid earlier this month although the commission was granted the right to review Seagram's earlier bid for Conoco. The FTC letter reflects the scars of the agency's fight over Du Pont.

"The comission had initially sought, and been granted, clearance to review the proposed acquisition of Conoco by Seagram," the FTC said in the letter to Assistant Attorney General for Antitrust William Baxter.

"After the department withdrew its grant of clearance, and during discussions concerning which agency should review Du Pont's proposed acquisition of Conoco, the commission's representatives consistently emphasized the agency's very considerable expertise with respect to the companies involved and the markets about which antitrust issues might arise," Clanton wrote.

"While the department's representatives also addressed these matters, the initial and principal in the department's presentation was a different consideration -- namely the department's desire to use this matter as a means to articulate certain of its general enforcement intentions for large mergers," the FTC stated in the letter.

After Mobile made its tender offer for Conoco, the two agencies once again met, with the FTC arguing that its staff had considerable expertise in "virtually every aspect of the domestic oil industry. Once again, the question of comparative expertise did not appear to be the decisive factor," Clanton wrote in the July 23 letter.

"Rather, the department conveyed its decision that it wanted to pursue the Mobile matter because it believed it should review all proposed mergers involving Conoco," Clanton wrote.

The interagency battle, which threatens to destroy what has been a relatively smooth working relationship between the two antitrust enforcement agencies, also looms as a large test for the beleagured commission, which is made up of two Republicans and two Democrats. James C. Miller III, an Office of Management and Budget official and a top Administration regulatory policy maker, has been nominated to become the agency's chairman in September.

The FTC has been the target of considerable Reagan administration criticism and the OMB asked Congress last spring to eliminate the FTC's antitrust authority through a series of budget cutbacks over three years.

Only congressional and small business opposition to the proposal by OMB Director David A. Stockman forced the administration to drop the plan. But Baxter has said that he favors eliminating the FTC's antitrust responsibilities.