The man, who cannot be named for legal reasons, is facing 16 charges of indecent assault and child rape relating to two daughters and a son, all of whom were under the age of 10 at the time of the alleged offending.

The man's wife told police the family fled war-torn Iraq in 2013 and lived in a refugee camp in Lebanon before coming to Australia in 2016.

The woman claimed she caught her husband in "inappropriate" situations with their children multiple times at the refugee camp and suspected he may have been sexually abusing them.

Her concern was further heightened when she allegedly discovered him naked in one of the girl's bedrooms later that year, prompting her to report the matter to police in February 2017.

Child abuse squad detectives interviewed the woman and her children however ultimately did not proceed with laying charges due to "insufficient evidence", court documents said.

(The man was prohibited from seeing or contacting the children via an apprehended violence order).

However, the case was re-opened in September that year when further allegations were raised.

Police interviewed the mother and children again, then referred the matter to the Office of the Director of Public Prosecutions for a review of the evidence.

Police were advised to proceed with laying charges this time and the man was arrested last week.

The charges relate only to offences alleged to have occurred after they arrived in Australia.

The man sought bail in Wollongong Local Court, with his lawyer casting doubt over the authenticity of the children's complaints.

She also said the man had no passport and could put up a surety of $5,000 to ensure he turned up to court.

However, Registrar Kirby Moore refused bail based on the seriousness of the case. The matter will return to court later this month.