"The good news is, this is not like Ebola. People don't die of Zika," he said in an interview on “CBS This Morning.”
"A lot of people get it and they don't even know that they have it," he added.
The proposal also includes a $250 million one-year increase in health funding for pregnant women in Puerto Rico, where a state of emergency has been declared because of the virus.
All 46 Senate Democrats sent a letter to the White House last week calling for an "urgent and aggressive response" to the Zika virus.
"By taking action now, we can make significant progress toward mitigating the impact of the Zika virus abroad and reduce the potential for Zika virus outbreaks in the United States," the letter said.
Asked whether athletes should consider skipping the upcoming Olympics in Brazil, where the Zika outbreak is believed to have originated, Dr. Anthony Fauci, director of the National Institutes of Health's National Institute of Allergy and Infectious Diseases, said his role is only to "give them the facts."
"That's something that I think is a very personal decision," he told reporters at the White House Monday. "As an infection, it isn't serious. The issue we're focusing on is the issue of pregnant women."
"I think we are clearly better prepared for an outbreak like Zika than we were a year or so ago," he continued.