MOSCOW (AP) _ President Mikhail S. Gorbachev on Tuesday promised Iranian Parliament speaker Hashemi Rafsanjani that the Kremlin will not damage Tehran's interests, Tass reported.

Rafsanjani met with Gorbachev soon after he arrived on an official visit to forge economic and other ties between the nations, the official Soviet news agency said. Rafsanjani is the highest ranking Iranian official to visit the Soviet Union since the 1979 Islamic revolution.

Gorbachev spoke warmly of Iran's revolutionary renewal, and Rafsanjani said Gorbachev's reforms and Iran's own strength will help improve relations, Tass said.

The Soviet leader said that although relations between the neighboring countries have not always fared well, ''there cannot be and will not be anything in our policy now that would damage Iran's interests.''

The leaders discussed prospects for settling conflicts in the Middle East and Afghanistan, and their attitudes toward other countries, Tass said.

Soviet television showed Rafsanjani leaning back in a relaxed pose across a long conference table from an earnest, energetic Gorbachev.

Rafsanjani, who before leaving Tehran recalled that Soviet empires always had coveted Iran, was reported to have listed areas of agreement between the two. They included universal disarmament, the question of foreign military in the Indian Ocean, a neutral Afghanistan and national self-determination as areas where the two could come very close.

Rafsanjani expressed hope before he left home that the visit will open ''a new chapter in Iranian-Soviet relations and in the history of the region,'' the official Islamic Republic News Agency said.

Tass said earlier: ''In the Soviet Union there is confidence that the visit by Rafsanjani will give fresh impetus to the continued progress of Soviet- Iranian relations ... and will help improve mutual understanding and strengthen cooperation between the two countries.''

Rafsanjani also is acting commander-in-chief of the Iranian armed forces and is expected to seek military aid from the Kremlin.

His delegation includes Foreign Minister Ali Akbar Velayati and Mohsen Rezaie, commander of the Revolutionary Guards Corps.

Economics Minister Mohammad Javad Iravani preceded Rafsanjani to Moscow to prepare some economic and commercial agreements, the Iranian agency reported.

Iran officially has a non-aligned foreign policy, but Rafsanjani said soon after Ayatollah Ruhollah Khomeini died this month that Iran's spiritual leader had told him to improve relations with Moscow.

With ties to the West strained, Tehran is looking to the Soviet bloc for help in rebuilding Iran after its eight-year war with Iraq.

Relations between Tehran and Moscow soured soon after the 1979 Iranian revolution when Soviet troops deployed to help the Afghan government fight Moslem fundamentalist guerrillas and with Iran's 1981 repression of the Tudeh Communist Party.

The Soviet Union was one of Iraq's major arms suppliers in the Iran-Iraq war, which ended in a tentative August truce.

Soviet-Iran relations improved when Soviet troops withdrew from Afghanistan.