Opposition Leader Bill Shorten has deflected questions why Labor MP David Feeney – who has been unable to provide documents proving he renounced his British citizenship before being elected – shouldn't immediately resign, saying it was now a matter for the High Court.

Asked about a second Labor MP, Susan Lamb, who is also facing serious questions about her eligibility for Parliament, Mr Shorten said on Thursday he is "disgusted" that she is being pursued over dual citizenship concerns despite her difficult personal circumstances.

The citizenship imbroglio has now dragged on for more than six months and lingering doubts over a handful of MPs have ensured that the issue will remain on the agenda for some months yet.

Mr Feeney, a Victorian factional ally of Mr Shorten, was referred to the High Court late last year after failing to produce evidence that he had renounced British citizenship. Mr Feeney has not resigned – which would force a byelection for his seat – even though Liberal MP John Alexander quit last year in similar circumstances when he was unable to produce renunciation documents.