WASHINGTON — Republicans are preparing an alternative healthcare bill to Democratic legislation, House Republican Leader John Boehner said, marking a shift in strategy as the full House is set to begin debate on the issue this week.

Mr. Boehner said Sunday the Republican bill would extend health-insurance coverage to "millions" of Americans but wouldn't try to match the scope of the House Democratic bill unveiled last week. The Democratic legislation, if passed, is estimated to expand coverage to more than 30 million Americans now without insurance. Its estimated gross cost is $1.055 trillion over 10 years.

"What we do is we try to make the current system work better," Mr. Boehner, of Ohio, said on CNN's "State of the Nation." He said the GOP bill would be less costly to taxpayers and involve less government intrusion into the healthcare sector, instead taking "a step-by-step approach" to expanding coverage.

It would, among other things, propose new limits on medical malpractice lawsuits and make it easier for individuals and small businesses to pool resources to purchase insurance.

Mr. Boehner said the Republican bill would also include a proposal to provide grants to states that use "innovative" solutions to expand insurance. He pointed to states that have created special "high-risk pools" to provide insurance coverage to individuals with pre-existing conditions

He said the bill wouldn't raise taxes, nor mandate that individuals and businesses purchase insurance, as the Democratic legislation does.

For months, Republicans have attacked the Democratic health plan, hammering at pieces of the bill — such as a proposed government-run health plan — and helping to stir public doubt over the initiative.

By unveiling their own legislation, Republicans will be able to coalesce around a concrete plan. But they also open themselves to potential criticism of their proposals.

Republicans have talked about a variety of alternatives to Democratic efforts on healthcare, but decided to put out their own bill after seeing details of the legislation unveiled by Democrats last Thursday. GOP leaders hope to offer the measure as an alternative during debate on the Democratic bill, and a spokesman for House Speaker Nancy Pelosi (D., Calif.) said Republicans would be allowed to do so.

In the Senate, where Democratic leaders are pushing a proposal to create a new government-run insurance plan, Sen. Joseph Lieberman, the Connecticut independent, made clear again Sunday that he opposed the idea. The senator said he wouldn't try to block debate on the bill, but signaled he would support any Republican efforts to block a vote on it.