Australia's Prime Minister Scott Morrison has warned his predecessor Malcolm Turnbull to stop undermining the government.

Australia's national broadsheet newspaper, The Australian, reported on Friday that Morrison's office has reached out to Turnbull, "seeking a detente after weeks of damaging leaks against the new Morrison government."

It came after Turnbull on Thursday called on the government to refer Minister for Home Affairs Peter Dutton to the High Court over concerns that he is in breach of the Australian Constitution and is ineligible to serve in parliament.

The appeal by Morrison's staff reportedly warned Turnbull that his social media commentary on the Dutton saga was "putting future government at grave risk."

Morrison succeeded Turnbull as PM after the governing Liberal Party in August voted to depose Turnbull as leader and install Morrison.

Turnbull retired from politics following the leadership ballot.