RECIFE, Brazil (Reuters) - Children born with abnormally small heads and brain defects linked to the outbreak of Zika virus in Brazil are also suffering serious damage to their eyesight and possibly their hearing, doctors said on Thursday.

Half of the 135 babies being evaluated at a rehabilitation center in the northeastern Brazilian city of Recife have limited vision due to deformed optic nerves and retinas, and many are cross-eyed, ophthalmologist Camila Ventura said.

"Their eyes are scarred for life," said Ventura. "Between 40 and 50 percent of them have serious eyesight defects."

The babies are some of the 3,700 cases reported in Brazil since last year of newborns with a neurological condition called microcephaly that is associated with the mosquito-borne Zika virus sparking a health scare across the Americas.

The surge in cases of the rare condition is unprecedented and scientists have yet to prove categorically it is caused by Zika. But they know the condition will handicap the development of the children who will have to struggle with learning disabilities and impaired motor functions.

Doctors at Recife's Altino Ventura rehab center are testing the babies' vision and hearing to determine what they are able to see and hear, before giving them therapy to stimulate their brains.

Daniele Ferreira Santos, 29, said her two-month-old son Juan Pedro could hear alright but was having difficulty seeing.

"I am very distressed. We do not know how badly he has been affected and whether there will be other problems," she said, trying to calm her agitated crying baby.

Ventura said the babies needed to have therapy to stimulate their eyesight in the first three to six months of their lives or else their vision would never improve.

In a letter to the editor published last week by the British journal The Lancet, Ventura and her team alerted the medical community to the eyesight problems found in Brazilian children with microcephaly thought to be caused by a Zika infection caught by mothers in the early stages of their pregnancies.

The World Health Organization (WHO) said on Thursday that the virus is "spreading explosively" and could infect as many as 4 million people across the Americas.

(Reporting by Anthony Boadle; Editing by Andrew Hay)