U.S. sees 10 mln more H1N1 vaccine doses next week

* Larger volumes of vaccine being produced in U.S.

* White House frustrated with slow pace of production

* Obama adviser sees "ample supply in very short order"

WASHINGTON, Oct 31 (Reuters) - Five drug companies are now increasing production of the vaccine for the H1N1 swine flu, and 10 million more doses are expected next week, Health and Human Services Secretary Kathleen Sebelius said on Saturday.

President Barack Obama on Friday expressed frustration about the slow pace of production of the vaccine, which has resulted in just 26.6 million doses as of Friday, far below earlier estimates of 40 million by the end of October.

Sebelius said those initial estimates were based on "overly optimistic" predictions by the five contracted vaccine makers for the U.S. market -- MedImmune, a unit of AstraZeneca (AZN.L), Sanofi-Aventis (SASY.PA), Australia's CSL (CSL.AX), GlaxoSmithKline (GSK.L) and Novartis (NOVN.VX).

But production was now increasing and vaccine doses were being shipped seven days a week, Sebelius told CNN.

"The good news is that we have, as of yesterday, 26.6 million doses out and around the country. We are expecting another 10 million doses next week," Sebelius said. "So the vaccine is beginning to roll in larger volumes. And it's being distributed as quickly as it comes off the line."

"It's being shipped overnight. We're getting it from producers seven days a week," she added.

HHS initially estimated that 20 million doses would roll out every week, but the companies are currently producing only about 10 million doses a week.

The latest count shows 114 children have been killed by the virus in the United States since April, during a time when there is usually virtually no influenza, according to the U.S. Centers for Disease Control and Prevention.

CDC researchers estimated this week that as many as 5.7 million people in the United States have been infected so far, with at least 1,300 deaths. The flu has been reporting in 48 states, an unprecedented level.

David Axelrod, Obama's senior adviser, told National Public Radio in an interview aired on Saturday that the administration "overpromised" the vaccine based on the companies' assurances.

But he said the problem was abating every day: "We believe that that is improving on a daily basis, and we're going to have an ample supply in very short order."

Sebelius told CNN there was now a good mix of the nasal vaccine and the nasal mist available after earlier shortages, and the government expected to make sufficient vaccine doses available "over the next several months."

The United States still planned to participate in an 11-nation program to donate H1N1 vaccine to developing countries, but only after the priority population in the United States had been vaccinated, Sebelius said.