South Australian Premier Jay Weatherill has reportedly apologised to the husband of a dead British man whose same-sex marriage is not recognised under Australian law.

Marco Bulmer-Rizzi had appealed to the UK and Australian governments to intervene after "outright discrimination" by Australian authorities which deemed his same-sex marriage null and void.

David and Marco Bulmer-Rizzi were on their honeymoon in Adelaide when David was killed in a fall. Credit:Facebook

His husband David Bulmer-Rizzi, 32, died suddenly on Saturday after falling down stairs and cracking his skull at a friend's home while the newlyweds honeymooned in Adelaide. Under South Australian law, Mr Bulmer-Rizzi has not had final say in any of the decisions around his husband's death because his marriage is not recognised in the state. Instead, David Bulmer-Rizzi's death certificate states "never married".

Mr Bulmer-Rizzi told BuzzFeed News on Wednesday that Mr Weatherill had phoned him directly and in the course of the 10-minute conversation, apologised for what happened, told him he would work on ways to change the legislation and eventually provide him with a new death certificate.