PHOENIX — The recession is taking another big bite out of the state budget, with a surge in the number of people who now qualify for taxpayer-provided health care.

New figures from the Arizona Health Care Cost Containment System show an additional 21,000 people were signed up just this past month. Total AHCCCS enrollment now stands at about 1.2 million — about one out of every six state residents.

And the rate of growth of the program is outstripping population.

Tom Betlach, the agency’s deputy director, said the program added 120,700 people in the last 12 months. That computes out to about 11 percent.

By contrast, the last time the U.S. Census Bureau checked, the year-over-year population increase was just 2.3 percent.

Most immediately, Betlach said, that means AHCCCS will need $250 million more next budget year than the agency had predicted just several months ago. Now, the state will need to come up with nearly $1.9 billion.

The timing comes as lawmakers already are struggling with a $3 billion gap between anticipated tax collections and expenses.

AHCCCS is the state’s version of Medicaid, with the federal government picking up about two-thirds of the total cost.

Generally speaking, states have some leeway in determining who is covered. But a 2000 ballot measure approved by voters guarantees free care to anyone below the federal poverty level — currently $18,310 for a family of three — meaning lawmakers cannot cut back enrollment.

Jeff Tegen, the agency’s budget administrator, said the economic downturn and the subsequent job losses are largely to blame for people now seeking their health care from the state. And Tegen, in a memo to lawmakers, said he does not see things getting better any time soon.

“While there are some economic indicators that seem to be showing signs of improvement, employment continues to deteriorate,’’ he wrote. He pointed out the jobless rate in March, the most recent figures, his 7.8 percent, which is up three points over last April.

Tegen isn’t the only one predicting higher unemployment. Dennis Doby, senior director of research administration at the state Department of Commerce, said he expects the April unemployment figure, to be released later this month, to top 8 percent.

And Doby said he is expecting Arizona to top 9 percent and even go into the low 10 percent range before turning around.