For more on this deception, see the article, "Was President Truman Duped?," which contrasts Harry S. Trumanís Diary entry for July 25, 1945, with the official bombing order he signed on the same day, and also with the minutes of the May 10-11, 1945, meeting of the Targeting Committee which show that the Committee favored bombing a city with a large population over bombing a purely military target.
Truman delivered his speech from the White House at 10 P.M. Washington time on August 9, 1945. By this time, a second atomic bomb already had destroyed the city of Nagasaki. Because of the great length of the speech, most of which dealt with Germany, only the relevant paragraph is quoted here.
The world will note that the first atomic bomb was dropped on Hiroshima, a military base. That was because we wished in this first attack to avoid, insofar as possible, the killing of civilians. But that attack is only a warning of things to come. If Japan does not surrender, bombs will have to be dropped on her war industries and, unfortunately, thousands of civilian lives will be lost. I urge Japanese civilians to leave industrial cities immediately, and save themselves from destruction. -- President Harry S. Truman, Radio Speech to the Nation, August 9, 1945
Source for speech excerpt: Public Papers of the Presidents of the United States: Harry S. Truman, Containing the Public Messages, Speeches and Statements of the President April 12 to December 31, 1945 (Washington D.C.: United States Government Printing Office, 1961) page 212. The full text also was published in the New York Times, August 10, 1945, page 12.