Declaring that New York’s government faces a crisis of public trust, Gov. Andrew Cuomo challenged the Legislature on Monday to pass a thorough clean-government program in the aftermath of Speaker Sheldon Silver’s arrest and vowed not to sign a budget this year that lacks a full slate of ethics reforms.

Scarcely a month into his second term as governor, Mr. Cuomo said it was time for Albany to make a choice: either ban outside income for lawmakers and force the Legislature to work full-time, or enact new rules for disclosing outside pay. And he called for stricter limits on legislators’ use of expense allowances and of their campaign funds.

“This has been a difficult month for the state of New York, the reputation of the state of New York,” Mr. Cuomo said on Monday at the New York University School of Law. Alluding to the death of his father on New Year’s Day, he said former Gov. Mario M. Cuomo would have been “outraged and angered” by developments in the capital.

Mr. Cuomo called public corruption a decades-old dilemma for New York, and he laid down a list of demands before the Legislature. He urged lawmakers to stop using campaign funds and no-questions-asked per diem allowances to pad their personal incomes, and to pass a constitutional amendment barring all those convicted of felonies from collecting government pensions.