Malcolm Turnbull has hit back at his successor after Scott Morrison criticised the former prime minister's performance during a diplomatic trip to Indonesia.

Key points: Mr Morrison told broadcaster Alan Jones Mr Turnbull spoke about issues not in his brief

Mr Morrison told broadcaster Alan Jones Mr Turnbull spoke about issues not in his brief Mr Turnbull tweeted the prime minister asked him to discuss trade and the embassy issue

Mr Turnbull tweeted the prime minister asked him to discuss trade and the embassy issue Mr Turnbull will make his first major media appearance on Q&A next Thursday

Mr Turnbull travelled to Bali to meet with President Joko Widodo at the request of Mr Morrison earlier this week.

During that trip he warned against Mr Morrison's plan to consider moving Australia's embassy in Israel from Tel Aviv to Jerusalem.

That prompted Mr Morrison to say on Thursday he would not send Mr Turnbull on any more diplomatic trips.

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Mr Morrison, in an interview with 2GB, said "issues of trade and other things" were "not really part of the brief" for Mr Turnbull's trip.

That prompted Mr Turnbull to take to Twitter to respond to the criticism.

"A few facts. @ScottMorrisonMP 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 @jokowi," he tweeted.

"There was a detailed paper on the issue in my official brief as well."

During his trip, Mr Turnbull said moving Australia's embassy to Jerusalem would provoke a "very negative reaction" from Indonesia.

This morning, 2GB radio broadcaster Alan Jones asked Mr Morrison whether there would be "more missions for this man to be able to go and spout his own, discredited views".

To that, the Prime Minister replied, "no".

But Mr Morrison said he would always act "with respect" towards the country's previous prime ministers "regardless of who they are".

"But I do think the exemplar of previous prime ministers about how they go about things post and outside politics is John Howard, and on Labor's side it's Julia Gillard," he said.

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Mr Turnbull took to Twitter again following media reports of his tweet about Mr Morrison and the Indonesian trip.

He insisted his first tweet was a "simple statement of fact" and criticised some of the reporting of it.

Mr Turnbull rejected suggestions he was "lashing out" or making a "public rebuke" of Mr Morrison.

"Neither characterisation is reasonable, but is objective reporting unadorned by sensationalism a thing of the past?" he said.

Mr Morrison, in a statement issued after Mr Turnbull's tweets, clarified Mr Turnbull's role as the head of the delegation attending the Bali conference.

"As head of delegation, he [Mr Turnbull] was briefed on appropriate responses on other issues that could be raised in any direct discussions with the President, in his role as head of delegation," Mr Morrison said.

"Accordingly there were briefings dealing with the issues he has referred to. The purpose of his attendance was the Oceans conference."

Sorry, this video has expired Former prime minister Malcolm Turnbull in Indonesia

The Prime Minister was widely criticised when he announced during the Wentworth by-election that Australia was rethinking its policy on Israel, including recognising Jerusalem as the official capital.

The move was seen by some as a deliberate pitch to the electorate's 13 per cent Jewish vote.

But Mr Turnbull has copped fire from Coalition MPs, who argue he did not do enough to help the Government win the by-election, which was triggered by his resignation after he was toppled by his own colleagues.

Earlier this week, he also "liked" a Twitter post that reported Newspoll figures that Mr Morrison's approval rating among voters had dropped.

Mr Morrison, when asked about that on 2GB, said "yeah, I'm aware of it. But I just brush it off".

Mr Turnbull will make his first major media appearance since losing the prime ministership, next Thursday, on the ABC's Q&A program.