Iran said in May it was suspending some of its commitments under the deal.
"Mr. Abe can be a great mediator to facilitate that (easing of oil sanctions).Japan has always respected Iran and Mr. Abe can play a very constructive role to calm the ongoing tension that can harm the (Middle East) region", said another Iranian official, who asked not to be named.
To achieve his aim of slashing Iran's oil exports to zero, the Trump administration has revoked waivers since May that had allowed some countries, including Japan, to continue buying Iranian crude and has effectively ordered countries to stop purchasing Iranian oil or face sanctions of their own.
However, Iran on Tuesday did release U.S. permanent resident Nizar Zakka, a Lebanese-born internet advocate imprisoned for years in Tehran on internationally criticized spying charges.
Tensions in the Middle East have risen in recent weeks, roughly a year after Trump's decision to leave the worldwide nuclear accord that led to the lifting of economic sanctions on Iran in exchange for its curbing of nuclear activities.
Before making the trip official, Japan carefully laid the groundwork.
January 1978 - Iranian Revolution begins.
Abe's two-day visit is the first to Iran for a Japanese premier since Takeo Fukuda in 1978.
September 1980 - Iran-Iraq war breaks out.
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Naturally reserved and reliant on her husband and a few close aides, she often says she is just quietly "getting on with the job". He champions a tougher stance on Brexit, saying Britain should leave with or without a deal by the new deadline of October 31 .
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April 2006 - Iran says it has successfully produced low-enriched uranium.
August 2002 - Allegations of Iran's nuclear development surface.
Meanwhile, US sanctions have cut off opportunities for Iran to trade its excess uranium and heavy water overseas, putting Tehran on course to violate terms of the nuclear deal regardless. We are comfortable with Prime Minister Abe speaking with Iranians.
September 2013 - Abe and Rouhani hold first summit in NY.
February 2016 - Japan and Iran sign investment agreement.
"Amid rising tensions in the Middle East, we plan to encourage Iran, a regional power, to move toward easing tensions at the top leaders' meetings", Abe's Chief Cabinet Secretary Suga Yoshihide said at a news conference on Tuesday, confirming plans floated by Japanese officials last month.
Several Japanese commentators quoted by Japan Times felt the current level of U.S. Yukiya Amano, the director-general of the UN's nuclear watchdog agency that monitors Iran's nuclear deal, acknowledged Monday that Tehran has increased its production.
Iran newspapers divided along conservative-reformist lines in their assessments of Abe's visit.