The Turnbull government has vehemently denied that police were rushed into arresting four alleged plane bomb plotters by a British threat to issue a public travel warning about Australia.

As police held the suspects for a third day, more details of the alleged network emerged with confirmation two men are related to a hardened foreign fighter in Syria and reports that another has a brother believed to be a senior Islamic State figure.

Police raided five properties and arrested four men on Saturday and have claimed they planned to put a homemade bomb on a plane, though as of Tuesday night no charges had been laid.

Abu Dhabi-based Etihad Airways issued a statement on Tuesday saying it was helping Australian police with the investigation.