Washington, D.C. ? Health insurance companies, facing the threat of a government health plan, offered on Tuesday to reduce rates for millions of women and accept close federal regulation of their industry.

The higher premiums now affect 5.7 million women, many of them self-employed people who must buy their own coverage.

The industry is trying to head off creation of a government health plan that would compete with them to 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.

A Senate panel is crafting sweeping legislation to overhaul the nation’s $2.5 trillion health care system.