At the World Bank’s annual meetings last year in Morocco, the organization’s new president, Ajay Banga, outlined a sweeping vision for how he wanted to rid the world of poverty while keeping the planet habitable.

Four months later, Mr. Banga, who assumed the top job last June, is confronting his first big management test and some early signs of unrest that have little to do with his aspirations to modernize the bank and supercharge its ambitions to combat climate change.

The challenge is related to an investment that the World Bank made a decade ago in a chain of schools in Kenya. The educational project was partly funded through the International Finance Corporation, the bank’s investment arm. It became a source of controversy when allegations emerged in 2020 about widespread sexual abuse at the schools, prompting an investigation by the bank’s internal watchdog.

The executive board of the I.F.C. has been reviewing a revised “action plan” that could take effect as soon as this week.

In recent months the World Bank’s leadership has been engaged in fraught deliberations over how much responsibility to accept and whether to compensate the victims. The debate has divided the countries that are invested in the bank and put a spotlight on Mr. Banga, who will be responsible for finalizing and carrying out the action plan.

The case has drawn the scrutiny of development experts and lawmakers, amid suggestions that the World Bank failed to police how its money was being used and even took steps to cover up wrongdoing.