WASHINGTON  President Obama, whose vilification of insurers helped push a landmark health care overhaul through Congress, plans to sternly warn industry executives at a White House meeting on Tuesday against imposing hefty rate increases in anticipation of tightening regulation under the new law, administration officials said Monday.

The White House is concerned that health insurers will blame the new law for increases in premiums that are intended to maximize profits rather than covering claims. The administration is also closely watching investigations by a number of states into the actuarial soundness of double-digit rate increases.

“Our message to them is to work with this law, not against it; don’t try and take advantage of it or we will work with state authorities and gather the authority we have to stop rate gouging,” David Axelrod, Mr. Obama’s senior adviser, said in an interview. “Our concern is that they not try and, under the cover of the act, get in under the wire here on rate increases.”

The law does not grant the federal government new authority to regulate health care premiums, which remains the province of state insurance departments. But with important provisions taking effect this summer and fall, the Obama administration has repeatedly reminded insurers  and the public  that it will expose industry pricing to what the health secretary, Kathleen Sebelius, has called a “bright spotlight.”