Monal Vachhani's son Aneev has only ever seen his grandparents on FaceTime.

Azadeh Oskouipour's heart has broken as the federal government allows international tennis players and Hollywood movie stars to enter the country - but not her US-based parents.

These are the realities for three Canberra mothers who have been separated from their loved ones after Australia's international border slammed shut in March last year.

Government rules allow "immediate family members" of Australian citizens and permanent residents to apply for exemptions to enter the country. However, parents aren't classified as "immediate family members", meaning they've been blocked from visiting their children in Australia for more than a year.

With Australia's border to remain closed for the foreseeable future, more than 70,000 people have now signed a online petition calling for parents to be eligible for exemptions.

The three Canberra mothers brought their young children to Parliament House on Tuesday morning, appearing alongside independent MP Zali Steggall before she tabled the petition later in the afternoon.

During question time on Tuesday, Home Affairs Minister Karen Andrews appeared the open door to allowing exemptions for parents, saying there were a "number of investigations that are taking place at this time".

Ms Steggall, who represents the Sydney-based electorate of Warringah, called for a compassionate solution for desperate families as she warned that Australia's strict border rules could exacerbate a skills shortage.

She acknowledged that allowing more arrivals would put further strain on Australia's quarantine hotels, but said the federal government had had 14 months to create a system that could cope.

"If we cannot have a system where parents of Australian residents and citizens who are contributing to our society, who are paying their taxes and ensuring we have the front-line services we need, are not able to have a very basic human right of support from their parents - we have a problem Australia," she said.

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Ms Robinson, an audiologist who lives in Canberra on a skilled migrant visa, said she wanted to return to work after giving birth to daughter Lucy four months ago.

But she said that wasn't possible without support from her UK-based parents, forcing her young family to consider a permanent move back home.

"She is four months now and there is no roadmap for reopening [the border] and I have no idea when they [grandparents] will ever get to meet her," she said.

"My parents are getting older and older, so there is that worry in the back of your mind - will they ever even get to meet her?"

"I've thought quite seriously about moving back to the UK. I'm here in Canberra on a state-sponsored visa because Canberra has a shortage of audiologists and now I'm potentially thinking about leaving - it just seems mad".

Ms Vachhani said her parents in India had been fully vaccinated and were more than happy to cover the cost of flights and hotel quarantine.

"We don't want to risk people here, but government really does need to build more quarantine facilities so it can return [people] in a safer way," she said.

Ms Oskouipour said if seasonal workers and international students could be allowed back into the country, so should the parents of citizens and permanent residents.

She expressed anger and frustration at the various travel exemptions that have been granted throughout the pandemic, including to players, coaches and officials at this year's Australian Open in Melbourne, while parents have remained shut out.

"Every time I read this kind of news it makes me very upset, more down, more disappointed, more feeling that there really is no hope - there is no light at the end of the tunnel," she said.

Ms Robinson, seated beside her, added: "It shows that this government cares about the economy and nothing else".

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