Scott Morrison says Mr Turnbull was supposed to focus on oceans while he was in Bali for a conference, but Mr Turnbull claims he was told to raise the Jerusalem dispute in briefings.
Former prime minister Malcolm Turnbull has taken to social media to correct the "facts" on his recent Bali trip, after Scott Morrison criticised his predecessor for raising the Jerusalem embassy controversy and said he would not be given any more foreign "missions".
Mr Turnbull, while attending a global conference in Bali earlier this week, noted Indonesia held "serious concern" over the Australian government considering moving its embassy in Israel.
"There is no question, were that move to occur, it would be met with a very negative reaction in Indonesia. This is after all the largest Muslim-majority country in the world," Mr Turnbull told reporters.
Asked on 2GB Radio on Thursday whether Mr Turnbull would be sent on further missions, Prime Minister Scott Morrison said "no".
He said Mr Turnbull was supposed to focus on oceans, and issues of "trade and other things" were "not really part of his brief".
But the former prime minister questioned that account on Twitter.
"A few facts. Scott Morrison asked me to discuss trade and the embassy issue in Bali and we had a call before I left to confirm his messages which I duly relayed to [Indonesian president Joko Widodo]. There was a detailed paper on the issue in my official brief as well."
The government floated the prospect of shifting the embassy during the final week of by-election campaigning in Mr Turnbull's former seat of Wentworth, where more than 12 per cent of voters are Jewish.
While the Liberals suffered a devastating swing against them in Wentworth, Mr Morrison has insisted the government is still considering the potential move.
The announcement was met with concern in Muslim-majority Indonesia. One leading human rights researcher told SBS News he predicted riots and boycotts of Australian products if the move went ahead.