Globally more than 700 people are known to be infected.
Person-to-person transmission has been confirmed in six countries.
But in cases outside Mexico, the effects of the virus do not appear to be severe.
There are estimated to be more than 300,000 pigs in Egypt, but the World Health Organisation says there is no evidence there of the animals transmitting swine flu to humans.
Pig-farming and consumption is concentrated in Egypt's Coptic Christian minority, estimated at 10% of the population.
Many are reared in slum areas by rubbish collectors who use the pigs to dispose of organic waste. They say the cull will harm their businesses and has renewed tensions with Egypt's Muslim majority.
On Saturday, health officials began the slaughter in earnest, moving in on a Cairo slum where rubbish collectors are said to keep around 60,000 pigs.
The slaughter is expected to take around a month.
Officials now say the cull is aimed at bringing order to the country's pig-rearing industry, so that in future animals are not reared on rubbish tips but on proper farms.
The government has been criticised for overreacting to the threat, but it was also criticised for responding too slowly to the bird flu crisis two years ago.
When bird flu appeared in the country in 2006 mass culls were carried out but at least 22 humans died from the disease.
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