The Bush administration said Tuesday that more than 2.6 million people had voluntarily signed up for Medicare's prescription drug benefit in the last 30 days, pushing the total voluntary enrollment to 3.6 million.

Michael O. Leavitt, the secretary of health and human services, cautioned beneficiaries that they might still encounter problems when they tried to use the new benefit for the first time.

Since the drug coverage took effect on Jan. 1, many low-income beneficiaries have been overcharged, and some were turned away from pharmacies without getting their medications because the pharmacies could not confirm their enrollment. 

The problems have been so widespread that more than 20 states have stepped in to pay drug claims that should have been paid by the federal Medicare program.

In a conference call with journalists on Tuesday, Mr. Leavitt said: "We are likely to see these problems on an ongoing basis until everyone has used their card at least once. From that point forward, it should be much smoother."

The secretary said that caseworkers in the 10 regional Medicare offices would solve problems for any beneficiaries who could not get their medicines.

In addition to those who voluntarily signed up, 10.7 million people have been automatically enrolled by the federal government or by health maintenance organizations.

Utah, Mr. Leavitt's home state, said Tuesday that it would cover drug costs for low-income Medicare beneficiaries who could not get their prescriptions filled. "We would rather pay for their drugs than for their hospitalization," said Dr. David N. Sundwall, executive director of the Utah Department of Health.
Gov. Arnold Schwarzenegger of California, a Republican, said Tuesday that older people were still having difficulty.

On Jan. 1, the federal government took responsibility for the drug coverage of low-income people dually eligible for Medicare and Medicaid. Mr. Schwarzenegger said this part of the new federal program had been operating with "an error rate of 20 percent" in California.

Since announcing emergency action to help its residents on Thursday, Mr. Schwarzenegger said, California has paid 34,000 drug claims that Medicare was supposed to pay.

Dr. Michael J. Sexton, president of the California Medical Association, said the federal program was "a bureaucratic mess." Michael J. Negrete, vice president of the California Pharmacists Association, said the federal response was "just not good enough." In effect, Mr. Negrete said, "it's like telling a person who's drowning, 'Hold on; we'll teach you how to swim.' "

Drug benefits are administered by private insurance companies under contract to Medicare. Over the weekend, the Bush administration told insurers to provide a temporary supply of any prescription that a person was previously taking, and it said that co-payments for low-income people must not exceed $5 for a covered drug.

Karen M. Ignagni, president of America's Health Insurance Plans, an industry trade group, said that insurers were "committed to providing a 30-day transition supply" of any drug that a Medicare beneficiary was taking before Jan. 1. 

Ms. Ignagni said in an interview Tuesday that insurers "will definitely be willing to reimburse states for drug costs" that the insurers would have paid if the program had been working properly. But she said she foresaw possible disputes over the amount of reimbursement because states had been paying more than the insurers would have paid on some claims.

Most insurers have lists of covered drugs, known as formularies. Under federal policy, Medicare drug plans are supposed to provide a one-time refill of prescriptions for new subscribers, even if the drugs would not ordinarily be covered. In the transition period, beneficiaries can appeal seeking coverage of such drugs, or doctors can rewrite prescriptions to comply with formularies.

Mr. Leavitt said that some problems were to be expected at the start of a big new program. "When there's change, there's an opportunity for things to go wrong," he said. "We are fixing them one pharmacy, one beneficiary at a time." 

With caseworkers and other federal employees available to help on toll-free telephone numbers, he said, "no senior should leave the pharmacy without the prescription drugs they need."