(Reuters) - A conservative opponent of affirmative action policies who has backed major court cases challenging the consideration of race in college admissions has a new target for potential litigation: Coca-Cola Co's law firm diversity policy.

Lawyers for a group founded by Edward Blum sent a letter to Coca-Cola's new general counsel this week demanding the company rescind a recently announced policy requiring its law firms staff its matters with diverse lawyers or risk losing pay and business.

Blum, who has long worked behind the scenes to line up plaintiffs challenging racial policies that benefit people of color, said Wednesday that his group, Project on Fair Representation, is preparing to back a lawsuit if Coca-Cola does not do so.

"It is our hope that Coca-Cola quickly suspends the racial quotas that have been imposed by their former general counsel," he said. "Failure to do so will likely lead to polarizing and costly litigation."

Coca-Cola had no immediate comment. The letter was written by C. Boyden Gray, a former White House counsel to President George H. W. Bush now at Washington, D.C.-based Boyden Gray & Associates.

The policy was announced in January by the Atlanta-based beverage giant's then-general counsel, Bradley Gayton, and said its firms must commit to having at least 30% of each billed associate and partner time be from diverse attorneys.

That included people of color, LGBTQ people, women, and people with disabilities, but at least half of a firm's diverse partner and associate billed time had to be from Black lawyers specifically.

Firms failing two quarterly reviews on team diversity face a non-refundable 30% reduction in fees until the firm's commitment is met. After that, the firm could lose Coca-Cola as a client.

But the policy's future has come into question after Gayton abruptly resigned last week after just eight months on the job, taking a new position as an outside consultant to Coca-Cola's chief executive.

The company said before Blum's letter was made public that its new general counsel, Monica Howard Douglas, is "fully committed to the notions of equity and diversity in the legal profession" and will be taking time to review any plans.

In an interview, Blum said he hoped Coca-Cola would end the policy. But if it does not, he said several small law firms that would have been affected by it are prepared to sue.

While not a lawyer, Blum, a former stockbroker, has been at the forefront of pursuing cases over affirmative action policies aimed at addressing the country's legacy of discrimination against Black people and other people of color.

He previously backed a lawsuit by a white woman challenging the affirmative action admissions policies of the University of Texas, leading to a 2016 Supreme Court ruling upholding the consideration of race in college admissions.

Blum is now hoping the 6-3 conservative Supreme Court reexamines the issue with a more recent case by a different group he founded called Students for Fair Admissions that is challenging Harvard University's consideration of race in undergraduate admissions.

In the letter to Coca-Cola, Boyden contended that the company's law firm policy violated the Civil Rights Act of 1866 by promoting racial discrimination in private contracting.

"Decades of case law have held that--no matter how well intentioned--policies that seek to impose permanent racial balancing are prohibited," Boyden wrote.

He also faulted the policy for requiring Black lawyers to be responsible for 15% of a firm's billed time, roughly tracking the Black proportion of the U.S. population, even though only 5.9% of U.S. lawyers are Black.

He cited press reports that Coca-Cola had paused the policy following Gayton's departure as a "welcome development," but said "more is needed."