Nicola Sturgeon was asked by Glasgow SNP MSP Sandra White what discussions the Scottish Government has had regarding providing assistance for those facing homelessness following the withdrawal of accommodation and support services.
The charity, Y People lost the contract to house asylum seekers and is unable to continue its policy of not evicting those who have been unsuccessful in their asylum application.
The organisation, formerly known as the YMCA, has written to those affected telling them of the situation, leading to alarm among many asylum seekers, and concern among politicians.
Ms White is hopeful that Holyrood will be able to work with the city council to ensure people are not left sleeping rough with no food or income.
Ms Sturgeon said it was a matter for the UK Border Agency and the UK Government at Westminster.
She said: "If asylum seekers are not adequately and properly supported, then obviously that often has a knock on effect to agencies operating in devolved areas of responsibility.
"The Scottish Government will continue to seek assurances from the UK Government that all action that is appropriate will be taken in this area."
Ms Sturgeon added it was in no-one's interest to see asylum seekers destitute.
Ms White wants to see health and social services used to ensure no-one is left destitute.
She said: "We can do something about it, if we have people on the streets in need of services.
"While we do not have responsibility or asylum cases we do for their social and health care needs.
"The Scottish Government has to step in and do something. If the council has to provide services then Holyrood can help with costs and work together so we don't allow people to be out on the streets with no food."