Thank you for your question! The president would often release a written statement and then verbalize parts of it for the benefit of the media and newsreels. This is the case for the president's statement of August 6, 1945. President Truman authorized the release of the full statement in Washington, DC, while he was traveling back from the Potsdam Conference on the USS Augusta. Then, aboard the Augusta, he verbalized portions of the statement for the news media. The most extensive audiovisual we can find at the Truman Library is available in the National Archives Catalog here: https://catalog.archives.gov/id/23630. This footage is in the public domain; no permission is needed to use this material. We kindly ask for credit if possible: 111-ADC-9865, US Army Signal Corps, National Archives and Records Administration.
For more information about the decision to use the atomic bomb, please see the resources on the Truman Library's website: https://www.trumanlibrary.gov/library/online-collections/decision-to-drop-atomic-bomb