LOS ANGELES  When Bernhard Punzet opened the dreaded envelope from Anthem Blue Cross one recent Saturday, it ruined his weekend.

Although he had no known medical problems, the company was raising the premium on his individual health insurance policy by 34 percent, to $254 a month. The policy for his partner, who is 12 years older, would rise 36 percent, to $369.

“Ten percent I could have rationalized,” said Mr. Punzet, 34, a financial controller for a Los Angeles recruiting firm. “But a 34 percent increase? I don’t even have any data points for that, nothing to compare it to. I’ve never seen anything go up 34 percent.”

With health care negotiations stalled in Washington, the Obama administration is seizing on the seething fury felt by Mr. Punzet and nearly 700,000 other Anthem customers in California who have received notices of increases that average 25 percent. About a quarter of them are seeing leaps of 35 percent to 39 percent, the company said, at least four times the rate of medical inflation.