The new, higher figure was first reported by The New York Times. It includes deaths caused by complications related to swine flu, including pneumonia and bacterial infections.
Until now, the Centers for Disease Control and Prevention had conservatively put the U.S. swine flu death count at more than 1,000. Officials said this week they're working on an even more accurate calculation.
"This comes down to an accounting issue," CBS News medical correspondent Jennifer Ashton said on the "Early Show" Thursday.
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The CDC - noting that estimating flu cases is extremely difficult because many infected people do not see treatment - estimates that between 14 million and 34 million cases of 2009 H1N1 occurred between April and October 17, 2009. The mid-level in this range is about 22 million people infected with 2009 H1N1.
The cases resulted in between 63,000 and 153,000 H1N1-related hospitalizations during the same time period, the CDC said.
Ashton reported Monday after visiting the Center's headquarters in Atlanta that the CDC's death count of 1,000 was likely a gross underestimation.
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"The Early Show" at the government's battle with H1N1, the tracking system in place doesn't always give a full picture of the pandemic.
The numbers being reported are from flu model estimates - not the actual numbers, Dr. Thomas Frieden, director of the CDC, told CBS News.
"It's a little counter intuitive," Frieden said, "but the best way to estimate the total burden of illness is not to count the cases, but to estimate them based on the best available science."
Ashton said the current report of 4,000 deaths is in the "predictable range" and it's important to follow the trends more than the actual numbers.
Ashton pointed out, however, that things are very different when reporting pediatric flu deaths. She said states are required to document each case with the CDC, and every week the updated numbers are an accurate reflection of the entire country.