Agitated by activist investors, ExxonMobil this week promised substantial new investments to combat the effects of climate change and announced the election of a new director as part of what it called a broader board “refreshment.”

However, activist investor Engine No. 1 LLC said the changes were insufficient. The San Francisco firm said it stood behind a move to nominate four board members in an effort to establish a board independent from management. It said directors should more aggressively pursue long-term strategies that include actions to combat climate change and drive sustainable long-term earnings.

“ExxonMobil shareholders deserve a board that works proactively to create long-term value, not defensively in the face of deteriorating returns and the threat of...