The world's biggest oil company emerged bruised but victorious from a bust-up with the billionaire Rockefeller family today as an effort to foist green initiatives on ExxonMobil failed to capture wholehearted support from shareholders.

Preliminary figures suggested that 39.5% of Exxon's investors backed a motion demanding the appointment of an independent chairman to stimulate debate about global warming on the company's board.

A resolution calling on Exxon to set limits on its operations' greenhouse gas emissions won 30.9% support, while a proposal to adopt a policy backing renewable energy only captured 27.4% of shareholders' votes.

The poll, at the company's annual meeting in Dallas, demonstrated that a sizeable chunk of Exxon's investor base is uncomfortable with the Texas-based company's hardline attitude towards climate change and alternative energy.

But the environmental vote barely budged from last year's level, in a disappointment to the Rockefellers who have since campaigned vigorously for change.

The family describes itself as Exxon's longest standing shareholder – the company's roots lie in the Standard Oil exploration empire which was founded by their ancestor, John D Rockefeller.

A smattering of protesters wielded banners outside the meeting in Dallas with slogans such as "people before profits" and "oil: the new black death". A small plane flew overhead urging a boycott of the company and police used bomb-sniffing dogs to heighten security.

Exxon's chairman and chief executive, Rex Tillerson, assured critics that he took all of their contributions seriously and that he accepted that environmental attacks were delivered in good faith.

He insisted the company was awake to the challenge of climate change: "We have the same concern as people around the world – to provide the world with its energy needs while reducing harmful emissions."

But Tillerson repeated Exxon's mantra that the demand for energy is set to rise 40% by 2030 – and that oil and gas will be needed to satisfy 60% of this sum.

Arguing that wind, solar and biofuels lack technological scale, he said the way to make "meaningful environmental improvements" was to find more efficient ways of delivering existing fuels.

His remarks failed to satisfy a large contingent of environmental advocates. One speaker, Stephen Viederman, accused Exxon's directors of checking in their responsibilities as parents and grandparents at the boardroom door.

"Exxon is acting like a dinosaur in not adapting to a changing environment. ExxonMobil-asaurus will disappear," said Viederman.

A Franciscan friar from Milwaukee, Michael Crosby, quoted a German proverb, "it was always this way", to sum up Exxon's attitude.

"But it isn't always going to be this way and we know it," said Father Crosby. "Things are changing and we have to adapt in this company."

Exxon's assumptions of future energy consumption were questioned by members of the Rockefeller family who suggested that projected growth in demand from developing countries could not materialise if those nations face weather catastrophes from global warming.

Neva Rockefeller Goodwin, an economist, described Exxon's approach as "significantly flawed" in failing to anticipate improvements in alternative fuels: "If energy technologies develop at the pace demonstrated by telecoms or the internet over past decades, they will seriously undermine Exxon's assumptions in demand for petroleum."

Exxon's board stonewalled almost every question by simply referring shareholders to the company's written responses.

A handful of speakers leapt to the board's defence. One investor, Ron Johnson, said his Exxon shares had risen 28-fold in value since he bought them in 1979 and had helped to fund his two children through college.

"Some of our distinguished shareholder colleagues seem to have lost sight of why we hired you," he told the board. "That is, to make us money."