The US is expected to ask Tokyo to send its navy to the strategic waters off Iran's southern coasts.
Japanese media have said Washington's proposal could be on the agenda during US national security adviser John Bolton’s visit to Tokyo this week, Presstv Reported.
"We have a long tradition of friendship with Iran and I've met with its president any number of times, as well as other leaders," Abe said at a press conference on Monday after his coalition's victory in parliament's upper house election held on Sunday.
"Before we make any decisions on what to do, Japan would like to make every effort to reduce tensions between Iran and the United States," he said.
The premiere added that Japan needs to gather information on what the US is thinking and what it hopes to accomplish with the new coalition.
Sources said the United States was struggling to win its allies' support for the initiative to heighten surveillance of the vital Middle East oil shipping lanes because of fears it will increase tension with Iran.
Tensions began after several oil tankers were suspiciously targeted near the Persian Gulf last month, with Washington and its staunch regional ally Saudi Arabia quickly blaming Iran for the suspicious attacks. However, Iran has denied all the charges warning neighbors against false flags by "foreign players."
Last month, Abe traveled to Iran carrying a message from Trump for direct negotiations with no preconditions. However, Iran turned down he offer, with Leader of the Islamic Revolution Ayatollah Seyyed Ali Khamenei telling the Japanese PM that the American head of state was not "worthy" of a response.
Paris and Berlin urge no escalation of tensions
Separately, France and Germany stressed the need to avoid any possible escalation following Iran’s seizure of a UK flagged oil tanker in the Strait of Hormuz. The call came after UK Foreign Secretary Jeremy Hunt spoke with his French and German opposite numbers on Sunday.
On July 19, the IRGC Navy captured British oil tanker Stena Impero for violating international maritime laws when crossing the high-traffic Strait of Hormuz.
"Both ministers agreed … that safe passage for vessels through the Strait of Hormuz is a top priority for European nations," the office of Hunt said in a statement.
UK Prime Minister Theresa May is to hold a meeting of the emergencies committee on Monday to discuss the issue.