It's possible in the far future. There's a difference between someone saying I'm sorry and the government officially saying it was a mistake. The consensus in the US is that the atomic bombings saved a ton of American and Japanese lives that would have been lost to an invasion. I think most Americans are sorry about the bombings but that's not the same as saying the decision was wrong. The Japanese indicated very heavily both through their fierce resistance over tiny islands and their propaganda that they were willing to fight to the last man, woman and child and that hyperbole is what led to Truman's decision. Did the Japs think the US could be forced into a peace settlement(true Unconditional surrender throughout history between great powers is rare and I understand why the Japs might have thought it was all talk) and was the US's ultimatum of destruction too vague to qualify as a serious warning? Yup but given the proportionality doctrine the bombings were in the best interest of the service members under Truman's command and the Japanese citizens of every other location in the country whose lives didn't end as a result. Under that logic the decision should not be apologized for and were for the benefit of the most people on both sides of the conflict.
Second bombing is more questionable than the first given that the first might have been enough to induce surrender in which case those deaths are for nothing and I'd somewhat agree with the spirit of the OP..
After the Hiroshima bombing, the three pri-war ministers of the Big Six (which ran Japan) told the Emperor it wasn't a nuke, just a big conventional bomb. Then after radiation readings confirmed it was an atomic bomb they changed their tune again, this time claiming there was no way the US could have made more than one.
The Big Six and Emperor only even openly contemplated surrender after the Nagasaki bomb. They met the morning of Aug 9 to discuss the Soviet declaration of war. During that meeting a messenger arrived with news that Nagasaki just got hit too.
At that point the pro-war ministers were still very a very limited surrender, with four completely unrealistic conditions. But other pro peace ministers started finally talking. Foreign Minister Togo admitted to everyone that, per the Emperor's secret orders, he'd previously been trying to open negotiation talks through the Soviet Union for a cease fire, but that was obviously out.
They cut that meeting, then met up later that night for a marathon night session, where the Emperor finally gave his opinion, that he wanted to end the war however. None of the Big Six were pro unconditional surrender, required per the Potsdam Declaration. Three pro peace wanted the emperor protected, three pro war wanted emperor protected, Japan retreats to pre Pearl Harbor territory,Japanese govt (meaning the Big Six) controls their disarmament and controls their own war crime trials to punish subordinates for following their own directives, and no occupation of Japan. Absolutely absord, but it was only after a night of bickering, into Aug 10, and after the Emperor brow beat them (he had caught them in another lie about defenses they swore were ready that hadn't been built yet), so it was only Aug 10 day that they decided unconstitutional surrender.
There is a theory that Truman could have added the stipulation to protect the emperor and they'd have surrendered earlier. The evidence to that is completely contradictory to the historical events. Its nonsense.