By Aaron Sheldrick

TOKYO, Feb 5 (Reuters) - Iran and Japan signed an investment agreement on Friday following the lifting of sanctions on Tehran last month, aimed at encouraging investment in the Iranian economy from Japanese companies wary of remaining U.S. restrictions.

Major international companies have been rushing to establish themselves in Iran as the country re-opens for business after the lifting of international sanctions but Japanese companies have been cautious.

"Iran has great potential for Japanese companies as an investment destination given its rich reserves of oil and natural gas and its huge market," Japan's foreign ministry said in a statement after the agreement was signed in Tokyo.

The agreement "improves legal stability of investment, will contribute to promotion of the reciprocal investment and human exchanges, and to further development of the economic relationship between the two countries," the ministry said.

With a market of 80 million people and annual output of some $400 billion, Iran is the biggest economy to rejoin the global trading system since the Soviet Union broke up over two decades ago.

Although many crippling sanctions have been lifted in return for compliance with a deal to curb its nuclear ambitions, some financial restrictions remain in place, which has kept Japanese companies on the sidelines.

"If any Japanese banks or other banks feel that they have some problems, immediately let us know," Mohammad Khazaee, Iran's vice minister of economic affairs and finance, told a gathering of about 200 Japanese business representatives on Friday.

"We have a channel of communication directly to the U.S. Treasury and to the U.S. Secretary of State," Khazaee said before exhorting Japanese companies to invest.

Washington still prevents U.S. nationals, banks and insurers from trading with Iran and also prohibits any trades with Iran in U.S. dollars from being processed via the U.S. financial system, a significant complication given the greenback's role as the world's main business currency.

Iran has 9.3 percent of the world's proven oil reserves, the fourth largest after Venezuela, Saudi Arabia and Canada.

It also has 18.2 percent of the world's natural gas reserves, bigger even than Russia's 17.4 percent share, according to the BP Statistical Review of World Energy.

(Reporting by Aaron Sheldrick; Editing by Tom Hogue) ((aaron.sheldrick@thomsonreuters.com; 81-3-6441-1320; Reuters Messaging: aaron.sheldrick.thomsonreuters.com@reuters.net))

Keywords: IRAN JAPAN/INVESTMENT