Health insurers would drop out of Obamacare if Congress repeals the provision that requires every American to purchase health insurance or pay a fine, the American Academy of Actuaries warned Tuesday.

"Insurers would likely reconsider their future participation in the market," the group said in a letter to Senate leaders. "This could lead to severe market disruption and loss of coverage."

The Senate version of the tax bill includes a repeal of the provision, known as the individual mandate. A Congressional Budget Office projection shows that doing so would result in 13 million more people becoming uninsured, but the agency is revisiting its methods. An analysis from S&P Global Ratings pegged the projection to be less than 5 million.

Insurers have insisted that they need the individual mandate or some other mechanism such as a waiting period to ensure that healthier enrollees will sign up for coverage.

The actuaries group called the individual mandate an "integral component" of Obamacare, noting that the law expects insurers to cover people with pre-existing illnesses without charging them more. The mandate makes the provision possible, the group wrote.

Other than leading to insurer exits, the agency said that removing the mandate would cause the prices of premiums to increase and would cause insurers to lose money.