WASHINGTON — With lawmakers poised to begin a major push to reshape the nation's healthcare system, President Obama yesterday signaled new openness to the idea of the government requiring most Americans obtain medical insurance — a position likely to increase momentum behind the drive to create a coverage mandate.

At the same time, the president, who rejected such a mandate during the 2008 campaign, reaffirmed in strong terms his determination to offer a government-run healthcare plan as an alternative to private insurance.

"I strongly believe that Americans should have the choice of a public health insurance option operating alongside private plans," Obama said in a two-page letter to Sens. Edward M. Kennedy, D-Mass., and Max Baucus, D-Mont., who are leading efforts to develop healthcare legislation. "This will give them a better range of choices, make the healthcare market more competitive and keep insurance companies honest."

Obama also indicated he was receptive to a new requirement that large businesses share in the cost of providing health insurance. And he called for at least another $200 billion in cuts to the federal Medicare and Medicaid insurance programs for senior citizens and poor families to pay for expanded coverage. This would be in addition to $300 billion in cuts requested earlier.

The letter came as the White House intensified its effort to build momentum for a major healthcare overhaul this year. Obama has asked Congress to send him a bill by October.