The Potsdam ultimatum
On July 26, Truman and other allied leaders issued The Potsdam
Declaration outlining terms of surrender for Japan.
The atomic bomb was not mentioned in the declaration.
On July 28, Japanese papers reported that the declaration had been
rejected by the Japanese government. That afternoon, Prime Minister
Kantaro Suzuki declared at a press conference that the Potsdam
Declaration was no more than a rehash (yakinaoshi) of the Cairo
Declaration and that the government intended to ignore it
(mokusatsu).
The statement was taken by both Japanese and foreign papers as a
clear rejection of the declaration.
Emperor Hirohito, who was waiting for a Soviet reply to
noncommittal Japanese peace feelers, made no move to change the
government position.
On July 31, he made clear to Kido that the Imperial Regalia of
Japan had to be defended at all costs.
In early July, on his way to Potsdam, Truman had re-examined the
decision to use the bomb. In the end, Truman made the decision to
drop the atomic bombs on Japan.
His stated intention in ordering the bombings was to bring about a
quick resolution of the war by inflicting destruction, and
instilling fear of further destruction, that was sufficient to
cause Japan to surrender.
source
http://en.wikipedia.org/wiki/Atomic_bombings_of_Hiroshima_and_Nagasaki