All the cases were in or near the Aljunied area in the southeast of the city-state, and most were foreign workers from a nearby construction site owned by GuocoLand, where testing for the virus is now complete, the health ministry said in a statement.
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Singapore, a major regional financial centre and busy transit hub, which maintains a constant vigil against the mosquito-borne dengue virus, reported its first Zika case in May, imported by a middle-aged man who had been to Brazil.
One of the cases discovered on Sunday involved a Singaporean man who works at the GuocoLand site but who lives outside the Aljunied area. The NEA inspected more than 900 premises around his home on Monday.
One local pharmacy worker said she ran out of mosquito repellent, and was concerned about delays in getting fresh supplies.
'I feel afraid'
The Zika virus, carried by mosquitoes, was detected in Brazil last year and has since spread across the Americas.
Zika causes only a mild illness in most people. But infection during pregnancy can lead to severe brain-related birth defects. It has been linked in Brazil to more than 1,600 cases of microcephaly, where babies are born with abnormally small heads and brains.
Singapore's health ministry said around three dozen mosquito breeding habitats had been destroyed so far in the main Aljunied cluster.
Authorities have urged those living and working in the risk areas, especially pregnant women, to monitor their health and seek medical attention if they are unwell.
Regional health experts said the Zika virus is likely to be significantly under-reported across tropical Southeast Asia as local health authorities fail to conduct adequate screening.
Malaysia and Indonesia have stepped up protective measures following the Singapore outbreak, intensifying checks on people arriving from Singapore and introducing thermal scanners at airports and border checkpoints.