ALBANY — The latest scandal to hit the State Assembly has engulfed Speaker Sheldon Silver, the Legislature’s most powerful Democrat, as Gov. Andrew M. Cuomo and other elected officials on Tuesday called for an investigation into the Assembly’s handling of sexual harassment claims against a prominent assemblyman, including a secret settlement payment of more than $100,000.

Even as Assemblyman Vito J. Lopez, the man at the center of the scandal, agreed to give up his power base as chairman of the Democratic Party in Brooklyn, it was Mr. Silver’s decision to make the payment and keep the allegations against Mr. Lopez secret that drew the most outrage. Public advocacy and women’s groups, and even some Democratic lawmakers, expressed shock that the state would pay so much without public disclosure. Governor Cuomo — who had previously called for Mr. Lopez’s resignation over a separate set of allegations — became the most prominent voice calling for an ethics investigation as well.

The growing scandal led Mr. Silver to say that he had been wrong to approve the settlement. He said that he had previously endorsed the view of his counsel’s office that if an employee bringing a harassment claim requested confidential mediation, then the Assembly would accede to that request and not refer the claim to the Assembly’s bipartisan ethics committee.

“I take full responsibility in not insisting that all cases go to the ethics committee,” he said in a statement. “While that opinion is both legally correct and ethical and can result in a resolution sought by complaining employees, I now believe it was the wrong one from the perspective of transparency.”