TOKYO — Naoto Kan, the embattled Japanese prime minister, is likely to step down by early next week, a cabinet minister said on Tuesday, a long-expected resignation that will nevertheless bring uncertainty to a country still reeling in the aftermath of its natural and nuclear disasters.

Japan’s economics minister, Kaoru Yosano, quoted Mr. Kan as saying that he believed that his cabinet would resign and that a new prime minister would be chosen by next Tuesday. Ministers were told to “do their best with their remaining affairs and prepare for a handoff,” Mr. Yosano quoted Mr. Kan as saying at an informal cabinet meeting Tuesday.

Even before the March 11 earthquake, tsunami and nuclear accident, Mr. Kan, 66, had been unpopular, criticized for his perceived haplessness in both foreign and economic policy. Blunders in response to the disasters have brought Mr. Kan more disapproval, including a delay in admitting that the accident at the Fukushima Daiichi Nuclear Power Plant was far worse than previously announced.

His subsequent attempts to steer Japan away from nuclear power — a direction Japanese voters have seemed to support — have not been enough to reverse his sliding popularity ratings, or mollify heated criticism from the opposition and even from those within his own ruling Democratic Party.