New Delhi, Sept. 1 -- Just two months into his tenure as chair of HDFC Bank Ltd., Rajiv Kumar wasted little time in pushing for changes at India's most valuable bank.

He outlined several measures to Chief Executive Officer Sashidhar Jagdishan: accelerate loan growth, get more aggressive on technology, address the legacy issues, and replace some of the senior executives surrounding the CEO, people familiar with the matter told Bloomberg News.

Jagdishan, a veteran of three decades at the bank, resisted some of the proposed changes. Rather than push out bankers he supported, he decided to step aside when his term ends next month, the people said.

The surprise decision, announced at a hastily convened board meeting Saturday, sent shock wav...