Upon the completion of the hydrographic survey of any stream system, the state engineer shall deliver a copy of so much thereof as may be necessary for the determination of all rights to the use of the waters of such system together with all other data in his possession necessary for such determination, to the attorney general of the state who shall, at the request of the state engineer, enter suit on behalf of the state for the determination of all rights to the use of such water, in order that the amount of unappropriated water subject to disposition by the state under the terms of this chapter may become known, and shall diligently prosecute the same to a final adjudication: provided, that if suit for the adjudication of such rights shall have been begun by private parties, the attorney general shall not be required to bring suit: provided, however, that the attorney general shall intervene in any suit for the adjudication of rights to the use of water, on behalf of the state, if notified by the state engineer that in his opinion the public interest requires such action.