At least 4,000 swine flu deaths reported in U.S.

CDC: ‘Many millions’ have been sickened since outbreak began in April

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.

The CDC says "many millions" of Americans have caught the pandemic flu virus since it first appeared in April.

Separately, the World Health Organization said Thursday doctors shouldn't wait for lab confirmation before giving anti-viral drugs to pregnant women and other at-risk groups with suspected swine flu.

WHO medical officer Dr. Nikki Shindo said prescribing antivirals early to vulnerable people with clinical symptoms of swine flu can help lower the risk of serious complications.

Shindo said otherwise healthy people should only take drugs such as Tamiflu if their condition worsens rapidly and never as a preventive measure. "The vast majority" of people who catch swine flu will recover without medication or hospital treatment.

Shindo said that Ukraine, Afghanistan and Mongolia have reported their hospitals are being overwhelmed by serious cases.