The letter, which was due to be made public on Friday, represents a new front in the battle to halt the pipeline, weeks after President Donald Trump gave it the green light.
Representatives from banks involved are due to discuss the pipeline with tribal leaders on Friday, said people familiar with the matter.
Protesters have already targeted banks that have advanced funds to the project, which is being lead by Energy Transfer Partners.
Now, large investors have signalled that they will weigh in to support the campaign, citing the risks to the reputations of the banks involved if they do not address concerns about the pipeline's route.
Seventeen banks are identified in the letter, including Wells Fargo and Citigroup of the US and Société Générale and BNP Paribas of France.
"They control the purse strings," said Anne Simpson, head of corporate governance at Calpers. "Our intention is that they take action."
Signatories to the letter include four public employee pension funds of New York City, and private groups including Boston Common Asset Management and a host of religious orders. In all, the signatories control a total of $653bn in assets.
"We are concerned that if DAPL's projected route moves forward, the result will almost certainly be an escalation of conflict and unrest as well as possible contamination of the water supply," the letter says.
"Banks with financial ties to the Dakota Access pipeline may be implicated in these controversies and may face long-term brand and reputational damage resulting from consumer boycotts and possible legal liability."
The investors say that, while they understand that the banks providing the project finance have contractual obligations to the pipeline, "the extreme controversy tied to the project warrants their urgent action".
More than 92 per cent of the 1,172-mile route from North Dakota to Illinois has already been built, but opponents have been able to hold up a section running under Lake Oahe on the Missouri river.
At that point, the route passes within about half a mile of the border of the Standing Rock Sioux reservation. The tribe, concerned about the risks of a spill, began a legal action against the project and invited protesters from all over the world to support its campaign.
President Trump last month ordered that ETP be given a permit to finish the work, and the company estimated that oil could begin flowing in June. The US Army Corps of Engineers, which reviewed the route, concluded last year that the current one is the best option. After protests at Standing Rock last autumn the Corps put a temporary block on construction and demanded a new environmental impact assessment. It was that block that was lifted by Mr Trump.
But banks have come under mounting pressure over their role. Seattle City Council last week voted to cut ties with Wells Fargo and Bill de Blasio, the mayor of New York. has signalled support for a boycott.
Scott Stringer, the New York City Comptroller, issued a statement on Thursday night saying that building the pipeline on tribal lands was wrong and that the banks associated with it must act. "By funding this project, they are risking great reputational harm - especially if the conflict escalates. Alternatives do exist. We implore the banks involved to take meaningful action and develop a new plan that respects the tribe and the sovereignty of their land," he added.
Despite the protests, lenders have said they remain committed to helping finance the contentious project. "We have an obligation," Tim Sloan, chief executive of Wells Fargo, said last week.
"That credit facility was properly vetted and independently reviewed within Wells Fargo. We thought it made sense." It declined to comment directly on the investor letter on Thursday, but said the loans it had provided represented less than 5 per cent of the total.
Citigroup, the other US-listed bank named in the letter, did not have an immediate comment on the investor letter. It said two weeks ago that while it was "very concerned about the situation on the ground in North Dakota", the bank "cannot terminate this contract unilaterally".
Pension funds too have come in for criticism. More than 40,000 people signed a petition demanding that Calpers and Calstrs, the second-largest public fund in California, sell their holdings in ETP.
A bill has also been proposed in the California state assembly to require the two pension funds, which are estimated to have $100m in combined investments in ETP, from putting any additional money into the companies constructing or funding the construction of the pipeline.
Calpers has decided not to sell out of ETP, however; it is generally opposed to divestment as a strategy, saying it is better to stay invested and engage with companies.
The full list of banks identified in the letter is as follows: Bank of Tokyo-Mitsubishi UFJ, Bayern, BBVA, BNP Paribas, Citigroup, Crédit Agricole, DNB, ICBC, ING, Intesa Sanpaolo, Mizuho Bank, Natixis, Société Générale, SMBC, SunTrust Bank, TD Securities and Wells Fargo.
Copyright The Financial Times Limited 2017