WASHINGTON – Pushed by a dramatic increase in the number of Americans who will get insurance under the new health care law, total U.S. medical spending will continue to gallop upward, consuming nearly 20 percent of the economy by 2019, according to a new government estimate.

But because new savings in the law offset most of the cost of extending insurance to more people, the nation’s total health care bill is not expected to be substantially larger than it would have been without the overhaul.

“It appears that the Affordable Care Act will have a moderate effect on health spending growth,” said Andrea M. Sisko, the lead author of the closely watched study by independent economists at the Centers for Medicare and Medicaid Services.

The estimates, which parallel earlier analyses of the law, underline a major promise of the landmark legislation that President Barack Obama signed in March.

By 2019, nearly 93 percent of the population is projected to have medical coverage, compared with about 84 percent now. Without the law, the percentage of people with coverage was expected to dip to 83 percent over the next decade, according to the report.

Before passage of the law, the United States was projected to spend $4.5 trillion on health care in 2019, up from about $2.6 trillion this year. The overhaul is expected to push up the nation’s 2019 health care bill to $4.6 trillion.

That translates to an average annual growth rate of 6.3 percent over the next decade.

The continuing upward surge in total health care spending poses a challenge for Obama and others who championed the health care overhaul as a way to “bend the cost curve.” Republican critics of the new law, many of whom are promising to repeal it, have seized on earlier estimates of rising health care spending to cast the overhaul as a failure.

On an individual level, millions of Americans are still seeing their health care bills rise as insurance companies demand higher rates and employers pass along a growing share of their health care costs to workers.

The overhaul includes numerous provisions designed to relieve this cost pressure on consumers, including those to improve the quality of medical care and make the health care system more efficient.