The following answer is based upon information in Downfall, by Richard Frank and Racing the Enemy by Tsuyoshi Hasegawa. These are two of the best books on the final days of the Pacific side of World War II.
In Japan, there was never a thought of surrendering before Germany. In 1944, the German military attache in Tokyo reported that the entire country was mobilizing as the tide of war turned against it. He reported the determination of the "Japanese Army and the circles it influences to go through with the war without compromise on the side of Germany."
The Portuguese minister to Japan reported in May 1944 that "the fortification of coasts and mountains continues, giving the impression that this country, like Germany, is disposed to prosecute the war to its very end without the least probability of victory."
In June 1944, Swiss minister Camille Gorge observed, "Japan does not expect to win, but is still hoping to escape by prolonging the war long enough to exhaust [her] enemies."
As Frank concludes: "... no matter how desperate the situation, Japan intended to fight to the bitter end." This was apparent as early as spring 1944, before the beginning of the strategic bombing campaign.
By 1945, it was clear that things were nearing an end. Japanese minister to Switzerland Shunichi Kase reported in April to Tokyo that he had "rather concrete knowledge" of a plan for Hitler (or other top Nazi leaders) to escape Germany to Japan on a long-range aircraft. On April 12, the Japanese military and naval attaches in Germany asked for a long-range aircraft that could fly from Norway to Japanese territory (likely over the pole to Manchuria, overflying the Soviet Union). The plane was to carry a German assistant air attache and one other passenger. The flight did not take place.
Kase later pushed for peace from his post in Bonn, saying that he had interviewed three Swiss banking officials who said "Japan is not an object of world-wide detestation like Nazi Germany," and therefore should make a peace offer.
In late April, Tokyo radioed its officials in Europe, asking them to report "as fully as possible" on the last stage of resistance in Germany "in order to furnish reference material for the Decisive Battle." This was a reference to the expected invasion of the Japanese Home Islands. The attache in Lisbon was told to pay particular attention to the training of civilian militias and what effect the direct participation of the German High Command and Hitler in combat had on civilian morale.
Magic intercepts in spring 1945 revealed instructions from the Japanese foreign ministry to its diplomats in Moscow. They needed to know what Soviet intentions would be following the surrender of Germany. The cancellation of the Soviet-Japanese neutrality pact on April 5 was seen as a sign that the Soviet Union would enter the war sooner, rather than later. Secretly, Stalin had promised Churchill and Roosevelt that he would enter the Pacific war within three months of the German surrender.
On April 30, the Supreme War Leadership Council met and decided "to continue the war until the objective of the Greater East Asia War is achieved. To that end, Japanese diplomats were given instructions to try to feel out Soviet officials and see what the price would be to prevent the Soviet Union from entering the war. Barring that, they were to discern when and if the Soviet Union would enter the war.
Not until August 2 did these instructions shift, and diplomats began tentative feelers to see under what circumstances the Allies would end the war.
Publicly, Japanese officials announced their intentions to fight on to the conclusion of the war. Kantarō Suzuki, the Prime Minister of Japan, declared in a radio announcement on May 3 (the day after Hitler's suicide) that the Japanese people should continue fighting with the spirit of a kamikaze pilot.
Shigenori Tōgō, Japan's minister of foreign affairs, stated: "German actions [will] not affect the Empire's determination to pursue the war against the United States and Britain."
On May 9, the day after Germany surrendered, the Japanese government declared that its objective the war was self-preservation and self-defense, so therefore Japan should be even more determined to defend itself against the United States and Britain, regardless of the situation in Europe.