Mohammad Javad Zarif told Tasnim news agency that he sent a tweet saying: "Happy Rosh Hashana".
In a Twitter exchange that followed, he also distanced himself from the Holocaust denials of former President Mahmoud Ahmadinejad.
It comes amid confusion over whether new President Hassan Rouhani also tweeted "Happy Rosh Hashana".
A message came from a Twitter account thought to belong to Mr Rouhani earlier this week, but officials later said he did not have any such account.
Iran has a Jewish community of up to about 30,000, according to some estimates, though much lower than the population which numbered about 80,000 prior to the 1979 Islamic revolution.
The fact that Iranian leaders are congratulating Jews on the occasion of Rosh Hashana would not necessarily be controversial, say correspondents, but many in the international community are watching for signs that Mr Rouhani is seeking warmer ties with the West and Israel.
Senior politicians are often the victims of Twitter hoaxes, whereby other web users set up fake accounts in their name.
But in an interview given to Tasnim and published on Mr Zarif's Facebook page, the foreign minister confirmed he sent the "Happy Rosh Hashana" message because of Iran's Jewish community.
By Rana RahimpourBBC Persian Service
The timing of these messages on Twitter may signal a shift in Iran's diplomatic discourse.
A few weeks ahead of President Rouhani's trip to New York and Iran's first meeting with the IAEA since his election, it seems the new leadership is trying to present a more pragmatic and approachable side to the Islamic Republic.
Furthermore, this rare instance of Iran's foreign minister using Twitter to respond to the daughter of a senior politician in the US, a country with which Tehran has had no diplomatic relations for three decades, means Iran is attempting to distance itself from the radical views of the last president.
In summary, Iran's new administration appears keen to create a more benign atmosphere for negotiations.
He then had a response from Christine Pelosi, the daughter of Nancy Pelosi, Minority Leader of the US House of Representatives, who said: "Thanks. The new year would be even sweeter if you would end Iran's Holocaust denial, sir".
He replied: "Iran never denied it. The man who was perceived to be denying it is now gone. Happy New Year."
He was referring to Mr Ahmadinejad who, during his presidency, frequently claimed the Holocaust was a lie.
"We have condemned the killing of Jews by Nazis as we condemn [the] killing and crackdown on Palestinians by Zionists," Mr Zarif told Tasnim.
Mr Ahmadinejad's anti-Israel comments and Tehran's controversial nuclear programme helped contribute to Iran's increased isolation in recent years.
Iran has been the target of four rounds of UN sanctions and numerous UN Security Council resolutions calling on it to cease enrichment work amid fears it aims to develop nuclear weapons.
Iran has refused to obey, saying it intends to enrich only for power station fuel or other peaceful purposes.
President Rouhani on Thursday announced that the foreign ministry would take over nuclear negotiations with the West from the Supreme National Security Council.
The move makes it likely Mr Zarif - who has experience living in and negotiating with the West having served as Iran's envoy to the UN - will take over responsibility for the talks.
Talks with the International Atomic Energy Agency (IAEA) are resuming on 27 September.
Correction 10 September: The estimated size of Iran's Jewish community has been amended in this story.

Charlie Clift, 56, was last seen buying outdoor clothing on Tuesday 30 January in Fort William town centre.
Highland and Islands Police said they were increasingly concerned about Mr Clift's welfare.
Lochaber Insp Andrew Bilton said they were asking hikers to keep an eye out for him.
He said: "Given the lack of contact from Mr Clift and the decline in weather conditions, his family, friends and officers are understandably increasingly concerned for Mr Clift's welfare."
Iran's foreign minister has confirmed he sent a message on Twitter wishing Jews a happy new year.
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