One Nation senator Malcolm Roberts is under mounting pressure to prove he's eligible to stay in Parliament but is refusing to provide evidence he renounced his British citizenship before last year's election.

Despite previously insisting he has only ever held Australian citizenship, Senator Roberts - who was born in India to a Welsh father, potentially making him a British national by birth - now says he is "no longer a British or Indian citizen" and has "renunciation documents".

Senator Roberts has signed a statutory declaration that he is "a citizen of Australia only", and holds neither British not Indian citizenship. It also says that prior to becoming a One Nation candidate he "investigated" his eligibility under section 44 of the constitution, which has already caught out three senators this month.