A third bomb was in production, though it wouldn't have been ready until after the 15th. Truman specifically rescinded authorization for atomic bomb release prior to the 15th, though.
On August 10, 1945, one day after the second bomb was dropped on Nagasaki, General Groves, the director of the Manhattan project, sent a memo to Truman's chief of staff stating that they were ahead of schedule for the third bomb (another fat man), and it would be ready to drop as early as August 17th. Truman responded, via his chief of staff, that a third, or any further bomb, should not be dropped without his (the president's) express authorization. The text is as follows
The next bomb of the implosion type had been scheduled to be ready for delivery on the target on the first good weather after 24 August 1945. We have gained 4 days in manufacture and expect to ship from New Mexico on 12 or 13 August the final components. Providing there are no unforeseen difficulties in manufacture, in transportation to the theatre or after arrival in the theatre, the bomb should be ready for delivery on the first suitable weather after 17 or 18 August.
The hand written response was:
It is not to be released on Japan without express authority from the president