"As Foreign Minister, Mr Peters should act without hesitation by requiring the offending diplomat to leave the country."
Jewish community leaders want Ghahremani, first secretary of the Iranian Embassy, to be expelled after he spoke alongside Holocaust-deniers at an Auckland mosque in June. The comments have come to light after video of the speech was posted online.
Ghahremani said in his speech that the "anti-human regime" of Israel was trying to "deceive the world" and was fuelling terrorism and extremism to divert attention from the Palestine issue, reported Fairfax.
Other speakers at the event denied the Holocaust and called for the "surgical removal" of Israel.
On Tuesday, Race Relations Commissioner Dame Susan Devoy said "people who deny the Holocaust took place are many things, but most of all, they are liars".
Brownlee said Ghahremani had delivered "what was effectively a hate speech".
Peters has hit back at Brownlee, saying he is "alarmed that Mr Brownlee is seeking to chastise me for an action that he should have taken months before the election".
"We are heading into a new era and looking positively towards the future, and I can't possibly fix up every mistake and omission that the last National Government has made."
In response, Brownlee said he had not known about the comments in the speech when he was minister.
"As soon as I did know, had I been the minister I would have done something about it instantly."
A Ministry of Foreign Affairs and Trade spokesperson said they were aware of the reported comments made by Ghahremani.
"Clearly, we do not agree. These comments will be deeply offensive to many people in New Zealand and elsewhere. Following the publication, we called in the Iranian Ambassador to express our disappointment at the participation in the event by a diplomat from the Iranian Embassy.
"Although the diplomat's remarks focused on Iranian government policy, we have made it clear to the Ambassador that we do not expect foreign representatives to New Zealand to participate in events where hate speech could be used.
"New Zealand continues to encourage a constructive dialogue between Iran and the international community."
Brownlee was Foreign Minister from May until September's election. Shortly after he took over, then-Prime Minister Bill English issued a mild rebuke to Brownlee for indirectly criticising New Zealand's co-sponsorship of a UN Security Council resolution on Israeli settlements.
Israeli Prime Minister Benjamin Netanyahu recalled his ambassador after the resolution passed without dissent on December 24 last year.
Brownlee was sworn in as Foreign Minister in May and immediately wrote to Netanyahu expressing the hope of restoring the relationship, a move that was expected to happen soon after McCully left.
But in an interview on Radio New Zealand, Brownlee said the resolution had been "premature" and implied it should not have passed without Israel's support.
New Zealand was one of four Security Council countries that agreed to co-sponsor an Egyptian resolution condemning Israeli settlements in occupied Palestinian territory as undermining the two-state solution.
Egypt withdrew its sponsorship after being pressured by then President-elect Donald Trump but the other four did not. The United States did not exercise its veto.
Peters is strongly pro-Israel. As part of NZ First's coalition agreement with Labour, a Cabinet minute will be recorded "regarding the lack of process followed prior to the National-led government's sponsorship of UNSC2334".
That was agreed despite Labour strongly supporting the Security Council resolution on settlements.
