The White House has landed another big Republican voice in support of sweeping health care legislation: Gov. Arnold Schwarzenegger of California.

With the health care legislation headed for debate on the floors of both chambers of Congress, the Obama administration has stepped up efforts to win support from Republicans away from Capitol Hill, where G.O.P. lawmakers are overwhelmingly opposed to the legislation.

In his statement, Mr. Schwarzenegger did not endorse any specific version of the legislation. But he noted his own efforts at improving the health care system in California and urged bipartisan cooperation at the national level.

Here’s his statement:

As governor, I have made significant efforts to advance health reform in California. As the Obama administration was launching the current debate on health care reform, I hosted a bipartisan forum in our state because I believe in the vital importance of this issue, and that it should be addressed through bipartisan cooperation. “Our principal goals, slowing the growth in costs, enhancing the quality of care delivered, improving the lives of individuals, and helping to ensure a strong economic recovery, are the same goals that the president is trying to achieve. I appreciate his partnership with the states and encourage our colleagues on both sides of the political aisle at the national level to move forward and accomplish these vital goals for the American people.

In lining up Republicans to support legislative action on health care this year, the White House is using a strategy similar to one it employed during debate over the economic stimulus plan earlier this year. Moving to bypass Republican opponents in Congress, the administration reached out to governors, many of whom stepped up in support.

On Monday, Tommy Thompson, the former health and human services secretary in the Bush administration, one-time Republican presidential candidate and former governor of Wisconsin, issued a statement expressing similar support for health care legislation this year. So did a former Republican — and now an Independent — Mayor Michael R. Bloomberg of New York City.