NEW DELHI—Vishal Sikka resigned Friday as chief executive of Infosys Ltd., citing a resistance to change at the company that deteriorated into ugly accusations of mismanagement at India’s second-largest software and outsourcing company.

The Bangalore-based company said Mr. Sikka had the support of the board but had been harassed into leaving by Infosys founder N.R. Narayana Murthy, who it claims tried to slander Mr. Sikka in letters to the media.

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