Brazil says the number of babies born with suspected microcephaly or abnormally small heads since October has now reached nearly 4,000.
In the worst affected area, about 1% of newborns have suspected microcephaly.
The Brazilian authorities believe the increase is caused by an outbreak of Zika virus. Just 150 babies were born with microcephaly in 2014.
The brain condition can be deadly or cause intellectual disability and developmental delays.
Colombia's health minister has advised women there to delay pregnancy.
Brazil's health ministry says there have been 3,893 suspected cases of microcephaly since October, when the authorities first noticed a surge, up from 3,500 in last week's report.
The link with Zika has not been confirmed, but a small number of babies who died had the virus in their brain and no other explanation for the surge in microcephaly has been suggested.
Zika is generally mild and only causes symptoms in one in five people. It is spread by the Aedes aegypti mosquito, which also spreads dengue and chikungunya.
Brazil is experiencing the largest known outbreak of Zika.
President Dilma Rousseff, visiting Recife in the worst-affected north-east of the country, said Brazilians needed to engage in the fight against the virus.
"Until we discover a vaccine, we will need to rely on the population to help us remove the conditions under which the mosquito reproduces," she said.
"In the meantime we need to provide all the assistance the children and their families require."
Forty-nine babies with suspected microcephaly have died, Brazil's health ministry says. In five of these cases an infection with Zika virus was found.
The Fiocruz research institute in Brazil says it has detected the virus in the placenta of a woman who miscarried in the first trimester of pregnancy - a step closer to establishing a clear link between the virus and the deformities affecting babies and foetuses.
Brazil's health ministry says that 90% of notified suspected cases of microcephaly are in the north-east - and 6% in the south-east, an area which includes Rio de Janeiro and Sao Paulo.
Rio de Janeiro is due to host the Olympics in August. The country is expecting 10,500 international athletes and many more spectators to attend.
The worst affected states in the north-east - the poorest part of Brazil - are Paraiba, Pernambuco and Bahia.
In Paraiba, the health ministry says that the number of babies born with suspected microcephaly works out as 114 per 10,000 live births - or more than 1 in 100 of all newborns.
Last week, Brazilian Health Minister Marcelo Castro said a new testing kit was being developed to identify quickly the presence of any of the three viruses spread by the mosquito concerned - dengue, chikungunya and Zika.
He also announced extra funds to speed up the development of a vaccine for Zika.
At the moment the only way to fight Zika is to clear stagnant water where mosquitoes breed, and to protect against mosquito bites.
There has been a sharp rise in the number of cases of Zika in several other Latin American countries.
In Colombia, more than 13,500 cases have been reported.
"We are the second country [in Latin America] after Brazil in the number of reported cases," said Health Minister Alejandro Gaviria.
He has advised women in the country not to get pregnant for the rest of the outbreak which, he said, could last until July.
In Bolivia, the authorities have reported the first case of a pregnant woman diagnosed with Zika.
"She has not travelled outside the country," Joaquin Monasterio, health chief for the eastern department of Santa Cruz, told AFP news agency. "This is a home-grown case."
The US Centers for Disease Control and Prevention issued an alert last Friday advising pregnant women to consider postponing travel to Brazil and other Latin American and Caribbean countries where outbreaks of Zika have been registered.
The travel alert applies to Brazil, Colombia, El Salvador, French Guiana, Guatemala, Haiti, Honduras, Martinique, Mexico, Panama, Paraguay, Suriname, Venezuela and Puerto Rico.