Richard Frank covers the question of Japanese conditional surrenders exhaustively in Downfall, which is quite highly recommended if you're interested in the various events that led to the atomic bombing, the Soviet invasion, and the Japanese surrender.

The quick answer is "the Japanese didn't offer a conditional surrender," though the US knew through codebreaking that the Japanese were definitely considering it. There were discussions with their ambassador in Moscow, Sato, who they wanted to have consult the Soviets in order to arrange for talks that they intended to lead to mediation. (They wanted to go through the Soviets because they perceived that there was no other power capable of standing between them and the US, because they wanted the implied threat of joining the Soviet sphere of influence to moderate Allied demands, and because they thought the Soviets were a neutral power and did not know that Stalin had already agreed to attack Japan.)

The Soviets did not agree to these discussions, insisting that the Japanese present concrete proposals. Sato repeatedly advised Tokyo that if they wanted to get anywhere with the Soviets, they had to actually decide what kind of peace proposal they wanted to pursue (in other words, before getting Soviet help to end the war, they first needed to decide to end the war.)

This was difficult, because there was a major split on the Supreme Council for the Direction of the War as to what proposals to put forth. Broadly speaking, the military members wanted to ask for no occupation and self-disarmament, as well as the retention of the Emperor, while the civilian members wanted to offer only the last condition.

The Japanese realized that the larger number of conditions would be a tall order for the Allies to swallow, and intended to offer them only after a "decisive victory" - one which caused a large number of Allied casualties and made the Allies rethink continuing the war. Their operations in the Philippines were intended to produce such a victory, but ultimately failed to do significant damage. The all-or-nothing emphasis on defense of Kyushu was another attempt at the same, but was forestalled by the events of August '45.