He also said Japan wants to make every possible effort to promote Middle East peace.
Citing a senior diplomatic source, Kyodo News Agency reported last week that Iran had proposed the visit and that the proposal was relayed during a two-day visit to Japan by Iran's Deputy Foreign Minister for Political Affairs Seyyed Abbas Araqchi.
Abe said Japan would make every effort to promote peace in the Middle East but did not specify when there might be a decision on sending Japanese seamen to the region to guard ships supplying Japan.
“I want to make diplomatic efforts as much as possible to help ease tensions and stabilize the situation in the region by continuing dialogue patiently,” he added."
“Japan, which has an alliance with the US and at the same time has maintained favorable relations with Iran for a long time, must forge its own path,” he said.
As one of those efforts, we are currently in talks about a visit by President Rouhani to Japan," he added.
Abe did not give details but local media reported the visit could take place on Dec. 20 or 21.
If the trip is confirmed, Rouhani would become the first Iranian president to visit Japan since 2000.
Japan maintains friendly ties with both the United States and Iran, and has tried to ease tensions between the two, which broke off diplomatic relations after Iran's 1979 Islamic Revolution.
Last year in May, US President Donald Trump abandoned the 2015 pact between Iran and world powers under which Tehran accepted curbs to its nuclear program in return for the lifting of sanctions.
Washington has reimposed sanctions aimed at halting all Iranian oil exports, saying it seeks to force Iran to negotiate in order to reach a wider deal. Tehran has rejected talks unless Washington returns to the nuclear deal and lifts all sanctions.
In May, one year after the US pullout, Iran began retaliating by scaling back its commitments to the deal.
The Nikkei business daily said last week the government would propose deploying one escort ship and a patrol aircraft from the Maritime Self-Defense Force on a one-year mission that could be renewed annually. It plans to finalize the plan by year-end, the Nikkei added.
Regional tensions have escalated after attacks earlier this year on oil tankers near the Strait of Hormuz, the crucial sea lane out of the Persian Gulf, and a strike on Saudi Arabian oil facilities, both of which the United States has blamed on Iran. Tehran has strongly rejected Washington’s accusations.
Japan has sought to play a mediating role between Iran and the US, with Abe traveling to Tehran in a bid to broker dialogue.
During the visit in June, Abe met with Rouhani and Iran’s Leader Ayatollah Seyyed Ali Khamenei, in which Ayatollah Khamenei reiterated Iran's stance that it has no intention of making or using nuclear weapons.
He met Rouhani again in New York during this year’s UN General Assembly.
Reuters and AFP contributed to this story.