"[I] realised that only a move to a country with such standards as New Zealand would entitle my son to a decent life.
"After that incident, he [Mr Forrest] left the hospital notifying me hours later that he was taking the kid with him, that he is going to leave the country for New Zealand and I do not have anything to do with the situation."
Mr Forrest said he was shocked when first told of Leo's condition but he never thought of abandoning him.
"They took me in to see him and I looked at this guy and I said 'He's beautiful, he's perfect and I'm absolutely keeping him'," he told ABC.
Babies born with disabilities face a tough life in Armenia and are often rejected by their parents, Mr Forrest said.
The couple filed for a divorce the week after Leo was born.
Ms Badalyan said: "I faced two options: to take care of the child on my own in Armenia, or to abandon my maternal instincts and extend the baby an opportunity to enjoy a decent life with his father in New Zealand. I went for the second option."
Mr Forrest could not be reached for comment tonight, and he told 3News he was "too exhausted" to respond to Ms Badalyan's statement.
He posted on the online fundraiser that he was "stunned beyond words" at the amount of money raised for him and Leo.
The money would be used to relocate to Auckland, and to give Leo "higher quality opportunities when it comes to education".
"We will use some of the money you've given to fund facilities and programs here in Armenia that will support future parents to keep their kids despite all disabilities, and to help better care for the special ones who end up away from their Mom & Dad.
"We'd also like to share the surplus funds with the only orphanage in Armenia that regularly takes abandoned Down Syndrome babies."
The fundraiser had captured the attention of media around the world and more than 17,133 people had donated.