More than 3,100 pregnant Colombian women are infected with the mosquito-borne Zika virus, President Juan Manuel Santos said on Saturday, as the disease continues its rapid spread across the Americas.

The virus has been linked to the devastating birth defect microcephaly, which prevents fetus' brains from developing properly. There is no vaccine or treatment.

There are so far no recorded cases of Zika-linked microcephaly in Colombia, Santos said.

"Today, there are 25,645 people registered infected with the disease in Colombia. Among them are 3,177 pregnant women," Santos said during a TV broadcast with health officials.

Brazil Zika Birth Defects

Dejailson Arruda holds his daughter Luiza at their house in Santa Cruz do Capibaribe, Pernambuco state, Brazil in December. Luiza was born in October with microcephaly and her mother was infected with the Zika virus after a mosquito bite. (Felipe Dana/Associated Press)

"The projection is that, [along] with the 25,000 cases we have, we could end up having 600,000 cases. That is what is being projected, before reaching a ceiling after which the decline starts, as such epidemics go," Santos said, adding there could be up to 1,000 cases of Guillain-Barre syndrome, a rare but serious condition that can cause paralysis and which some governments have linked to Zika infection.

Santos said the government was now uncertain about a previous projection for up to 500 cases of Zika-linked microcephaly, based on data from other countries battling the disease. Authorities will continue to investigate, he said.

The government will be working across the country to fight mosquitoes — fumigating and helping families rid their homes of stagnant water, the president said.

Colombian health minister Alejandro Gaviria has said he believes three deaths are connected with Zika.

The province of Norte de Santander had nearly 5,000 cases of the virus, more than any other in the country, an epidemiological bulletin from the national health institute published on Saturday showed.

Norte de Santander, along the eastern border with Venezuela, also had the highest number of pregnant women with Zika - nearly 31 per cent of total cases.

The country's Caribbean region, which includes popular tourist destinations Cartagena and Santa Marta, had more than 11,000 cases of the virus, the bulletin showed.

The government has said pregnant women with Zika are eligible to access much-restricted abortion services.

Many women struggle to find abortion providers even when they meet strict legal requirements and illegal abortions are widespread. On Friday, local media reported the first abortion because of Zika infection.

The government has urged women to delay pregnancy for six to eight months.

Unreported cases and patients with no symptoms of infection could mean that there are between 80,000 and 100,000 current Zika infections in Colombia, the government has said.

An estimated 80 per cent of those infected with Zika show no symptoms, and those that do have a mild illness, with a fever, rash and red eyes.​