Josh Frydenberg has publicly rebuked Christopher Pyne for commenting on the Coalition’s possible moving of Australia’s embassy in Israel, describing the defence minister as a “legend in his own lunchtime” as divisions within the cabinet intensify.

Pyne, who last month floated the idea of two diplomatic presences in the fraught territory, an idea he repeated on Monday, said it was up to his colleagues to explain why such a delicate foreign policy debate was being played out publicly.

“Well you’ll have to ask the people who are making those comments,” the defence minister said in an interview with ABC radio on Monday. “I can tell you there is a process in place. It’s the right process to determine whether the Australian embassy should be in the capital of Israel, which is West Jerusalem. Now if the shoe was on the other foot, it would be like Israel saying that they intend to put their embassy in Sydney and pretend that Canberra isn’t our capital.”

Pyne’s comments were in response to reports the minister for defence industry, Steve Ciobo, told his Indonesian counterpart there was “less than a 5% chance” of Australia moving its embassy, and Frydenberg’s advocacy to make the change.

Pyne has attempted to walk a diplomatic line in an increasingly loaded debate, which has spilled into the Morrison ministry.

Asked about Pyne’s comments, Frydenberg told 2GB he would leave his colleague to be a “legend in his own lunchtime”.

“I haven’t seen that but Chris has been giving his opinion freely ... I don’t know what got into his Wheaties this morning,” the treasurer told Ray Hadley. “Chris is his own person ... He is quite unique.

“He’s had plenty to say on it and I will make my comments judiciously and appropriately on all matter of issues.”

Under pressure during the recent Asean summit, the prime minister, Scott Morrison, told reporters Australia would finalise its discussion on the embassy issue by Christmas.

Pyne, who first raised the issue of two embassies ahead of the Wentworth byelection in the same week Morrison proposed discussing moving the Tel Aviv embassy, acknowledged the delicacy of Australia’s position in relation to its Muslim neighbours and trading partners who stand against the move.

Indonesia has since delayed signing a free-trade agreement with Australia, while Malaysia’s prime minister Mahathir Mohamad raised the issue with Morrison at the recent Asean summit in Singapore.

“That’s why we’re going through a proper process to determine whether it’ll assist the two-state solution for us to move our embassy from Tel Aviv to West Jerusalem on the side of Israel and, in the event that the Palestinians have a state of their own, which we hope that they will, and that’s the government’s policy, axiomatically, we would then establish an Australian embassy in East Jerusalem,” Pyne said on Monday.

“It’s an even-handed policy. But first we have to go through the process to see if it’s in Australia’s best interests.

“But I would stress that it’s not really up to other countries to determine our foreign policy.

“I know that Labor has subcontracted out foreign policy to other governments. We’ll make the decision about where our embassy is in Israel and no other country will determine that on our behalf.”

Frydenberg continued to push for the move.

“Scott Morrison has taken, I think, a principled position – that he is going to conduct a process, take input from the experts and resolve our position before Christmas,” he said. “I think that is the right thing to do.

“But I share John Howard’s view on this, that says, on principle, the embassy can move to Jerusalem. But more importantly, he said, that it is a basic tenet of our own foreign policy, that we decide where our embassies go.

“And I think John Howard’s intervention, is very, very important. Israel is alone, as you know, as a country, where Australia doesn’t have an embassy in its own capital.

“We already acknowledge the sovereignty over West Jerusalem, and the United Nations and some of its agencies have tended to have double standards on Israel compared to other countries.”

Following the broadcast, a spokesman for Pyne said Frydenberg had apologised for his comments and Pyne had accepted his apology.

On Sunday the trade minister, Simon Birmingham, called for calm among his colleagues, telling the ABC the government would make the decision on the best advice of security and diplomatic experts.