12/29/2014 08:44 EST | Updated 02/28/2015 05:59 EST

Bhavna Bajaj says she never vowed her son would stay in India

An Indian woman with permanent resident status in Canada, and who is trying to bring her three-year-old son here, admits she didn't disclose she had a child before her arrival in Ottawa, but disputes the assertion she had agreed to keep him in India.

Citizenship and Immigration Canada said Bhavna Bajaj repeatedly failed to disclose that she had a son, Daksh, before she came to Ottawa. The department said that after she arrived, she signed a document saying her son would continue to live with his grandparents in India.

Bajaj and her husband, Aman Sood, say they're fighting to change Canada's immigration laws after being separated from their son over what they have described as an application error.

The couple applied for permanent residency in 2011 when Bajaj was pregnant, they told CBC News. An immigration consultant had told them to head to Canada and sponsor their son after they arrived, they said.

In an emailed statement sent to CBC News on Monday, Citizenship and Immigration Canada said there was no mention of the son in Bajaj's 2011 application, even though he was born before the department received it in August 2011.

Son's existence not revealed until 2013, CIC says

Bajaj also didn't mention the baby at a medical exam in March 2012, or any time before her application was accepted in April 2012, the department said.

"It was only when she arrived in Canada in January 2013, and was interviewed by an officer, that she revealed that she had a son," reads the statement from spokeswoman Mary Jago. 

Citizenship and Immigration Canada also said Bajaj decided not to add the child to her application in January 2013, and that Bajaj "stated that the child would remain in India with his grandparents and signed a solemn declaration to support this statement."

The couple later applied to sponsor their son on humanitarian and compassionate grounds, and the department said it refused the application because "it appears that the child never resided with his parents and has continuously resided with his grandparents... [and is] living in an environment which was culturally and linguistically familiar to him, among people who had cared for him since birth."

Decision to not declare son based on legal advice

In a statement released Monday night, the couple said the decision not to declare the three-year-old in their application was "an honest mistake."

"We relied on the legal advice of the immigration consultant who told us that we could sponsor him once we settle down in Canada. We had the plan to sponsor him as soon as we get a place to stay and start working. We thought it would take a couple of months before we could sponsor him," they wrote.

The family also disputed the federal department's interpretation of what was in the "solemn declaration" Bajaj signed.

"Ms. Bajaj never signed any declaration which stated that her child would remain in India with his grandparents. There is no word 'grandparents', 'India' in declaration that we signed. We challenge the CIC to prove what it has claimed. If needed we will reveal the declaration the copy of which we have in our possession," they wrote.

The two also disputed the government's claim that they never resided with the child.

"The CIC is actually enhancing our agony by making unsubstantiated allegations against us. It is also trying to justify its action with logic that is not defensible," they wrote.

The two said that, despite the dispute, they still held out hope that the immigration minister could intervene.

"We believe that good sense will prevail and we will receive relief from the immigration minister."