Investors managing more than $2.5tn have warned oil firms and banks to shun moves by the US president, Donald Trump, to open the Arctic national wildlife refuge (ANWR) to drilling.

Companies extracting oil and gas from the wilderness area in Alaska would face “enormous reputational risk and public backlash”, the investors say in a letter sent on Monday to 100 fossil fuel companies and the banks that finance them.

Exploiting the area would also be an “irresponsible business decision”, the group argues, as global action on climate change will reduce oil demand and mean such projects have a high risk of losing money. An accompanying letter from the indigenous Gwich’in people say it would be “deeply unethical” to destroy their homelands.

The 19m-acre refuge is one of wildest places left on Earth and the largest area of publicly owned land in the US. It is home to a huge range of animals, including polar bears, snowy owls and the porcupine caribou on which the Gwich’in rely for food.

In April, the Trump administration began the process of opening the ANWR for oil and gas drilling, the first such move since 1980. Significant oil and gas reserves are thought to lie under the ANWR coastal plain and Prudhoe Bay, a major oil centre, lies close to the refuge’s western boundary. The Gwich’in name for the coastal plain is “Sacred place where life begins”, as it is the breeding ground of the caribou.

“Drilling in the ANWR is an exceedingly high-risk gamble that companies and investors should avoid,” said New York state comptroller, Thomas P DiNapoli, trustee of the New York State Common Retirement Fund, one of the investors that signed the letter. “A global low-carbon economy is emerging, driven by the growing opportunities for cleaner energy. We want the companies we invest in to help build that future, not destroy one of America’s last truly wild places.”

“There is no longer any doubt that climate change poses an acute risk not only to our collective way of life, but also to investments made in outdated and highly precarious forms of energy,” said Thibaud Clisson at BNP Paribas Asset Management, another signatory.

Bernadette Demientieff, executive director of the Gwich’in steering committee, said: “We call on oil companies and the banks that fund them to stand with the Gwich’in and leave this pristine and fragile place intact. The survival of my people depends on it.”

However, Alaska’s congressional representatives, who are all Republican, strongly support the drilling plan, suggesting it could bring in $1bn to state and federal governments in the next decade. When the plan to open the ANWR for oil and gas exploitation was announced, it was “the single-most important step we can take to strengthen our long-term energy security and create new wealth”.

Murkowski, also chairman of the Senate committee on energy and natural resources, said: “Responsible development is limited to just 2,000 federal acres – just one ten-thousandth of all of ANWR.”

But the letter from the Gwich’in steering committee says: “This place was originally set aside by President Dwight Eisenhower in 1960 as a refuge, not for development. Roads, pipelines, gravel mines, airstrips and other facilities that would be developed to support exploration and development on the coastal plain would undermine the wilderness character of the Refuge, fragment habitat and displace wildlife. And oil spills, which already occur on the North Slope, would harm fish and wildlife.”