More than 100 leading scientists' sent an open letter to the WHO saying that it'sunethical' to take the Games ahead. But it has made no changes in the Games' schedule.
There is no reason to delay or move the Games because of the mosquito-borne disease, said The International Olympic Committee (IOC).
Zika virus outbreak began in Brazil a year ago but transmitted to more than 60 countries and territories.
In the letter, the scientists say that though Zika's symptoms are mild it causes babies to be born with abnormally small heads and may also cause a rare and sometimes fatal neurological syndrome in adults.
The letter sent to WHO was signed by 150 international scientists, doctors and medical ethicists from institutions as Oxford University, Harvard and Yale universities in the United States.
The reasons they cited for the move or postpone of the Games were: the failure of a mosquito-eradication programme in Brazil and the country's "weakened" health system.
"An unnecessary risk is posed when 500,000 foreign tourists from all countries attend the Games, potentially acquire that strain, and return home to places where it can become endemic," cites the letter.
The biggest risk the experts fear is if athletes contract the virus and return home which has not yet suffered a Zika outbreak will be more fatal.
"Brazil is one of almost 60 countries and territories which to date report continuing transmission of Zika by mosquitoes."
"People continue to travel between these countries and territories for a variety of reasons. The best way to reduce the risk of disease is to follow public health travel advice," said the WHO, denying postponing of Games.
To this, the head of the US Centers for Disease Control and Prevention (CDC), said on Thursday that threat did not warrant halting the Games.
"There is no public health reason to cancel or delay the Olympics," Dr. Tom Frieden said.
He has urged the US to act more quickly to prevent pregnant women contracting Zika.
This article is copyrighted by Travelers Today, the travel news leader