ExxonMobil and Chevron investors sided with the oil giants on climate change at annual meetings on Wednesday, rejecting shareholder resolutions to push Big Oil in a greener direction.

Environmentalists had hoped positive momentum from last December's Paris climate accord would galvanize investors to prod the industry to begin the process of rethinking the oil business.

But persuading the largest portfolio managers of the need for Big Oil to reorient itself in light of shifting policies on climate change still proved difficult, with a majority of shareholders voting down a trio of climate proposals at both ExxonMobil and Chevron.

ExxonMobil chief executive Rex Tillerson said the oil giant recognizes the importance of climate change, but that it opposes solutions it views as unrealistic.

"We are not ignoring the risk that is out there," said Tillerson.

"We are grounded in the reality of the world today... and the reality of the technology today."

"Until we see (technological change), turning the taps off is not acceptable to humanity," said Tillerson.

But a longtime advocate of climate measures, Sister Patricia Daly of the Tri-State Coalition for Responsible Investment, said ExxonMobil was failing in its duty to show "moral leadership" on a crucial energy dilemma of the 21st century.

She dismissed Tillerson's acknowledgement of climate change as double-speak, absent action to back it up.

"As the world moves forward, ExxonMobil stands still," said Daly, who alluded to news stories over the last year that accused ExxonMobil of waging a deceitful publicity war against climate science.

"Decades have been lost... due in part to our company's campaign of disinformation."

- 'Stress test' vote closest -

At both ExxonMobil and Chevron, the closest vote among the climate-related measures was over a resolution proposed by New York state's retirement fund to require the oil companies to perform an annual climate "stress test" of how changing public policies affect assets and long-term business prospects.

Advocates argue that tough climate policies could lessen the value of fossil fuel assets, resulting in decisions to keep oil in the ground.

The measure scored support from 38.2 percent of ExxonMobil shares, according to preliminary results released at the meeting. The breakdown was similar at Chevron.

Advocates of the measure said the level of support was high enough to get the attention of the oil companies.

"A significant number of Exxon shareholders want the company to step up when it comes to climate change," said Pete Grannis, first deputy comptroller for the New York State Comptroller.

"Exxon has a responsibility to its investors to explain how it can adjust its business to meet the global effort to reduce fossil-fuel consumption. Investors need to know that Exxon is taking steps to protect its long-term value."

Support was much lower for two other climate measures, which concerned appointing an independent director at each company with expertise on climate change and taking steps to keep global emissions from rising more than two degrees Celsius (3.6 degrees Fahrenheit) above the pre-industrial level, a central goal of the 2015 Paris climate pact of nearly 200 governments.

At least three-quarters of shareholders voted against these proposals at both ExxonMobil and Chevron.