Vaccinations, widely seen as cost-effective, numbered more than 15 million in five years against measles, diphtheria, tetanus and pertussis, and 99 million against hepatitis B, yellow fever and hemophilus influenza B, which causes meningitis.
But experts in global vaccination programs said such claims were hard to validate because so many children in developing nations die of conditions for which no vaccine exists.
According to GAVI's website, most of the vaccinations were for prevention of hepatitis B, which can cause cancer and liver failure.
The vaccine was widely used, Lob-Levyt said, because it could be offered rapidly at reasonable cost. Hepatitis B, however, rarely kills children, and many African children die of other ailments long before the vaccine could have saved them.
"You can't say any life was saved until they are older," said William Muraskin, a professor of urban studies at the City University of New York and author of a book about GAVI.
Citing a recent study in the Lancet, Yamada agreed that rates of child mortality in much of Africa had been flat to worse due to such problems as diarrhea, malaria and pneumonia.
"We can't rest on our laurels," he said. "The low-hanging fruit didn't necessarily have the outcome that we would have hoped."
The foundation is supporting research on vaccines against pneumonia and diarrheal illnesses. If these become available, he said, "you'll start to see an impact on child mortality that may be the next phase of GAVI's success story."
The failure to support basic care as comprehensively as vaccines and research is a blind spot for the Gates Foundation, said Paul Farmer, recipient of a John D. and Catherine T. MacArthur Foundation fellowship, and founder of Partners in Health, which has received Gates Foundation funds for research and training.
"It doesn't surprise me that as someone who has made his fortune on developing a novel technology, Bill Gates would look for magic bullets" in vaccines and medicines, Farmer said. "But if we don't have a solid delivery system, this work will be thwarted.
"That's something that's going to be hard for the big foundations," he said. "They treat tuberculosis. They don't treat poverty."
Still, Farmer, who knows the Gateses, said they had a deep personal commitment to understanding and addressing the needs of developing countries. He said he expected the Gates Foundation to increase its support for health delivery systems.
Yamada called delivery of care "a key strategic issue for us." The foundation will not provide care, he said, but has begun to study regulation, financing and how markets can improve delivery.
"What we do is we catalyze" -- develop tools to help governments improve, he said. "We are not replacement mothers."
Piller reported from Lesotho, Rwanda, Switzerland and Seattle; Smith reported from Los Angeles. Times staff writer Edmund Sanders, staff photographer Francine Orr, data analyst Sandra Poindexter and researcher Maloy Moore contributed to this report.