President Truman seems to have been surprised by the second bombing, coming as it did so soon after the first. Intercepted Japanese reports of the damage on the ground at Hiroshima were just trickling in to American officials. Truman, who had written in his diary in late July that “military objectives and soldiers and sailors” were the target of the atomic bomb, “not women and children,” apparently confronted the reality of the weapon for the first time. The Secretary of Commerce, Henry Wallace, reported in his journal that “the thought of wiping out another 100,000 people was too horrible” for the President. “He didn’t like the idea of killing, as he said, ‘all those kids,’ ” Wallace added.

The day after Nagasaki, Truman issued his first affirmative command regarding the bomb: no more strikes without his express authorization. He never issued the order to drop the bombs, but he did issue the order to stop dropping them.

Above is the relevant part of the article. Here is a link to the actual strike order drafted by Groves and then given out by Gen. Thomas Handy, acting Chief of Staff