A message on the website says there is an unplanned system outage which is being investigated.
The service allows users to lodge a visa or citizenship application and check the progress of applications.
The department has released a statement saying the issues are not linked to those experienced by the Australian Bureau of Statistics.
The A-B-S has temporarily taken down its census site and launched an investigation after a series of "denial of service" attacks, believed to have come from overseas.
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