The United States and Britain joined Australia and Taiwan in advising pregnant women to avoid non-essential travel to the city-state, while a local health expert warned the infection rate would rise.
The Ministry of Health and the National Environment Agency said in a joint statement late today they had identified 24 new infections plus nine more detected as a result of testing previous cases, bringing the total to 115.
A pregnant woman was among those who tested positive for the virus.
"She will be referred to a maternal-foetal medicine specialist for counselling and advice."
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The Aedes mosquito-borne Zika, which has been detected in 67 countries and territories including hardest-hit Brazil, causes only mild symptoms for most people, such as fever and a rash.
But in pregnant women it can cause microcephaly, a deformation in which babies are born with abnormally small brains and heads.
Brazil, where the disease has become an epidemic, has reported 1,835 cases of microcephaly, the World Health Organization says.
Expectant mothers with male partners who have tested positive were also told to visit their doctors.
The environment agency also said it would expand its operations to eradicate mosquitoes and their breeding places at a potential new cluster in the suburb of Bedok North and urged residents to cooperate, warning it will enter "inaccessible premises" by force if necessary.
"Over time, we expect Zika cases to to emerge from more areas," Health Minister Gan Kim Yong said in the statement.
"We must work out a plan on the basis that there is Zika transmission in other parts of Singapore."
"We will continue to work with all relevant government agencies and implement any recommended precautionary measures as directed or deemed necessary," he said.