WASHINGTON — Health insurance companies are offering new concessions, including lower rates for millions of women, as they try to persuade Congress not to set up a government health plan to compete against them.

On Tuesday, the industry offered to do away with an insurance surcharge that affects 5.7 million women, many of them self-employed and needing to buy their own coverage. Insurers also offered to accept new consumer protections.

Insurers want to prevent the creation of a government health plan that would enroll middle-class workers and their families. President Barack Obama and many Democrats favor such a plan, but the companies say it would drive them out of business. Employer groups are also leery, fearing a public plan would entice young, healthy workers by offering lower premiums.

"We are not asking people to trust us, we are asking people to trust government," Karen Ignagni, president of America's Health Insurance Plans, told a Senate panel that is crafting sweeping legislation to overhaul the nation's $2.5 trillion health care system.

Although the bill won't be written for weeks, insurers and other interest groups are trying to shape it now.

Instead of a government plan as a check on their industry, insurers are offering to accept stricter government rules they contend would add up to a fairer marketplace and cut into the ranks of the 50 million uninsured.

"We are comfortable with that," Ignagni told the Senate Finance Committee at a session on how to cover the uninsured.

Finance Committee leaders want to bring a bill to the Senate floor this summer. The broad outlines will follow Obama's campaign proposal, which builds on the current system of shared responsibility among employers, government and individuals.