Most of the USD 589 million would be devoted to the Centers for Disease Control and Prevention for research on the virus and Zika-related birth defects, as well as the creation of response teams to limit its spread.
The National Institutes of Health would continue research into a vaccine and the US Agency for International Development would intensify efforts to fight the virus overseas.
Researchers fear Zika causes microcephaly, a serious birth defect in which a baby's head is too small, as well as posing other threats to the children of pregnant women infected with it.
White House budget chief Shaun Donovan and Health and Human Services Secretary Sylvia M. Burwell said on a conference call with reporters that the administration still needs the full request to fight both Zika and maintain vigilance on Ebola.
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They said agencies would not be able to achieve the full menu of Zika response steps without additional funding.
"We cannot wait for this supplemental. We cannot wait for the fall," Donovan said.
"There are real consequences and risks for waiting."
It also wants to preserve money to keep fighting Ebola should it flare up again.
The impending move comes as there's greater urgency to battle the Zika virus as summer weather leads to mosquito season and a potential broader spread of the virus.
Burwell said that there are 672 confirmed cases in US territories such as Puerto Rico and the United States, including 64 pregnant women.
Congress approved about USD 5 billion in 2014 to combat Ebola.
Voters' fears regarding Ebola were seen as hurting Obama's party in the 2014 midterm landslide.