"The director of immigration does not believe in our clients", Robert Tibbo, one of the lawyers of the refugees, said after the decision. During that time they may be detained and the children placed in foster care.
Two of the Sri Lankan refugees say they are being illegally pursued by police from their own country who travelled to Hong Kong in late 2016.
The leaked classified information revealed details of widespread surveillance activities by the U.S. government.
When the families took Snowden into their apartments, they didn't know who he was, only finding out when they saw his face on newsstands.
His whereabouts were a mystery during that time and it was not until a year ago that the role Tibbo and his clients played in sheltering Snowden was revealed.
The impoverished Philippine and Sri Lankan refugees helped the former National Security Agency contractor evade authorities in 2013 by hiding him in their cramped homes after he initiated one of the largest data leaks in U.S. history.
In an exclusive video message sent to CNN, Snowden made an appeal for people to help these families, who have also applied for asylum in Canada, by calling the Canadian Immigration Minister, the Canadian consulate in Hong Kong, or the Hong Kong government itself to petition on their behalf.
In 2010, Rodel sought asylum in Hong Kong allegedly because she was a victim of rape and abduction.
His whereabouts during the two weeks in Hong Kong remained unknown until fairly recently.More news: UEFA Europa League finalists to be revealed
Canadian barrister Tibbo said that the Hong Kong authorities were not complying with their global obligations.
"We now have less than two weeks to submit appeals before the families are deported".
After government screening, claimants found to be at risk of persecution are referred to the UN's refugee agency, which can try to resettle them to a safe third country.
The BBC quoted Marc-Andre Seguin, a Canadian lawyer helping the asylum seekers for their separate applications with Canada, as saying the Sri Lankans and Rodel might have been targeted by HK immigration.
But with fewer than one percent of cases successfully substantiated by city authorities, most refugees live in fear of deportation.
Tibbo is also trying to raise $15,000 to cover legal costs associated with appealing the Hong Kong government's decision.
The families' lawyers say the Hong Kong government rejected their applications because it believes the Philippines and Sri Lanka are able to protect them.
The migrants "now find themselves at dire risk if sent back to their countries", said Dinah PoKempner, general counsel at Human Rights Watch.