Calls for the company to do more to address climate change concerns and invest in renewable energy sources generally gather momentum in the days ahead of the company's annual meeting, scheduled for May 31 in Dallas this year.

The group, comprised of pension fund trustees from eight states and New York city, as well as eight other institutional investors, said they were concerned Exxon's handling of the climate change issue left it lagging behind its oil major peers such as BP Plc and Royal Dutch Shell Plc.

"Exxon Mobil is making a massive bet with shareholders' money that the world's addiction to oil will not abate for decades," Connecticut state treasurer Denise Nappier said in a statement. "As investors, we are concerned that Exxon Mobil is not sufficiently preparing for 'tomorrow's energy' and runs the risk of lagging significantly behind its rivals."

In response, Exxon said it has an ongoing dialogue with members of the group and is setting up a meeting in July to discuss these issues.

The July meeting will only be with Exxon staff, however, a spokeswoman for the investor group said, noting they are seeking an audience with the company's board.

"In part, our position includes the fact that we recognize that the accumulation of greenhouse gases in the Earth's atmosphere poses risks that may prove significant for society and ecosystems," Exxon Mobil said in a statement. "We believe that these risks justify actions now, but the selection of actions must consider the uncertainties that remain."