WASHINGTON  The health insurance industry said Wednesday that it would support a health care overhaul requiring insurers to accept all customers, regardless of illness or disability. But in return, the industry said, Congress should require all Americans to have coverage.

The proposals, put forward by the insurers’ two main trade associations, have the potential to reshape and advance the debate over universal health insurance just as President-elect Barack Obama prepares to take office.

In separate actions, the two trade groups, America’s Health Insurance Plans and the Blue Cross and Blue Shield Association, announced their support for guaranteed coverage for people with pre-existing medical conditions, in conjunction with an enforceable mandate for individual coverage.

In the absence of such a mandate, insurers said, many people will wait until they become sick before they buy insurance.