Tokyo's benchmark stock index rose briefly above the 30,000-mark on Tuesday for the first time in about five months.
Share prices continued rising on expectations the successor to Prime Minister Suga Yoshihide will come up with steps to spur the economy.
The Nikkei Average ended the day at 29,916, up 256 points, or 0.8 percent, from Monday's close.
It gained nearly 400 points at one stage.
Analysts say investors are also buying on optimism that coronavirus infections in Japan may have peaked.
The Nikkei 225 has been on an upward trend since late August. It has gained for seven straight trading days, rising about 8 percent over the period.