Kan told members of his party that he felt responsible for carrying through with leading the recovery. He made the comments ahead of a no-confidence vote in parliament submitted by the opposition that has deeply split his ruling party.
"Once the post-quake reconstruction efforts are settled, I will pass on my responsibility to younger generations," he said. "The nuclear crisis is ongoing, and I will make my utmost efforts to end the crisis and move forward with post-quake reconstruction works."
Kan, who became prime minister just a year ago, has been criticized for delays in construction of temporary housing for evacuees from the March 11 disaster, lack of transparency about evacuation information, and a perceived lack of leadership.
On Wednesday, the largest opposition group, the Liberal Democratic Party, submitted the no-confidence motion along with two smaller opposition groups.
Although his Democratic Party of Japan controls the powerful lower house of parliament, where the no-confidence motion was submitted, dozens of ruling party lawmakers have expressed concern with his leadership, creating a deep rift.
The motion and the ruling party split have further complicated Kan's efforts to unite the government behind his reconstruction plans, which involve a huge injection of funds and possibly tax increases.
He was seen as an uninspiring prime minister even before the earthquake with a popularity rating below 20 percent.