On Tuesday, Mr. Mehleb abruptly walked out of a news conference in Tunisia after a reporter asked a question about reports that he had been implicated in a separate corruption inquiry. Mr. Mehleb has been accused of involvement in a case in which former President Hosni Mubarak and his two sons were convicted of embezzling funds earmarked for the renovation of presidential palaces.

“The minister of agriculture resigns after a corruption case, and you appointed this minister. You are one of the accused, the main accused, in the corruption case known as the presidential palaces,” the reporter said in a video of the incident before Mr. Mehleb headed toward the door.

The cabinet’s resignation also illustrated a political dilemma facing Mr. Sisi, the former armed forces chief who took power during a wave of nationalist fervor following the military’s removal of Mr. Morsi. In spite of the significant cult of personality around Mr. Sisi, his government has failed to resolve a number of problems facing Egypt.

Those troubles include a steady deterioration in its security. The government has been unable to end a violent insurgency in the Sinai Peninsula in which militants have been carrying out ever more brazen attacks.

Egypt also faces deep economic uncertainty, disappointing hopes raised at a much-promoted international investment conference in March and the opening of an expansion of the Suez Canal in August. The stock market has swooned since the conference, which had been billed as a move to restart the economy after years of instability in the wake of the 2011 uprising that ejected President Mubarak from power.