Finance Minister Conor Murphy has been urged to confirm when Land Registry, which records property transactions, will restore full services.
Land Registry, part of Land and Property Services within the Department of Finance, closed its offices and phonelines in March at the start of lockdown.
The DUP's Gordon Dunne, a North Down MLA, and East Antrim MP Sammy Wilson said the public now needs to be informed of when full services will resume.
"We have constituents who cannot complete the sale of their home, complete the purchase of their new home, re-mortgage or complete mortgage drawdowns because Land Registry has practically stopped providing any service," they stated. "We understand that every organisation has had to take steps to protect its employees but after several weeks, the minister needs to publish what plans he has to bring the service back on stream."
The notice on the LPS website says that all offices and phone lines have been closed until May 11.
It also adds that LPS is focused on "supporting the Covid-19 Business Support Grant Schemes".
A spokesman for LPS said members of the public and solicitors have been able to contact it by email, while the Land Registry was also working with UK finance lenders and the Law Society "to introduce workarounds to enable property transactions to complete where essential".
Staff will be in the office from Monday next week.
And from May 11, Land Registry will also accept new applications by post.
Mr Dunne and Mr Wilson said that they appreciated that everyone was facing "extraordinary circumstances".
However, they added: "This is a case of people who need to provide shelter for themselves and their families.
"Lots of organisations are continuing to provide a service by facilitating working from home."