A cease-fire in the Iran-Iraq war and recent overtures by Iran toward the West have together raised speculation about the release of nine American hostages said to have been taken by Iran-backed elements in Lebanon.The Reagan administration now needs to pursue these opportunities - not only to free the Americans, but also finally to open the door toward constructive ties between the United States and Iran.

Even after a decade of tension and bitterness between the two countries, Iran shares certain interests with the United States and is not necessarily committed to remain an implacable foe.

The nation has a vast stake in international trade and already keeps impressive commercial accounts with countries such as Japan and West Germany. Iran has restored diplomatic relations with Canada and France and may soon resume relations with Great Britain.

Its acceptance of U.N. Resolution 598 suggests an intention to break away from diplomatic isolation and accept a place in the international community.

Meanwhile, Iran's agreement to end the war with Iraq may also signal moderation toward other Middle East states.

Clearly, there is opportunity for mending relations between the United States and Iran. The goal of improved ties should be not only freedom for nine Americans but also an end to the American hostage phenomenon altogether.

The time has come for the Reagan administration to consider restoring commercial and diplomatic ties with Iran.

Moreover, it should not dismiss out of hand Iran's recent offer to help obtain release of the U.S. hostages in exchange for return of Iranian assets withheld by the U.S.

Washington must not lose sight of the fact that these properties actually belong to the Iranians, and releasing these assets no longer involves any concessions or major policy reversals on the part of the United States, as it might have during the Iran-Iraq war.

The assets come in two forms. First, there are funds - the exact amount is in dispute, but is in the billions of dollars - awaiting settlement before a special tribunal in The Hague.

They are a holdover from the Algiers accord that ended the 1979-81 hostage ordeal, and President Reagan should move swiftly to arrange for their arbitration. Of course, various U.S. assets have been frozen by Iran, and these, too, must be part of any settlement.

Second, there is military hardware purchased under the shah of Iran. This equipment poses an awkward dilemma because the administration officially forbids supplying arms to Iran, and exchanging arms for hostages is considered repugnant for understandable reasons.

Yet times have changed. If an end to the Iran-Iraq conflict is well established, the Reagan administration must reconsider its Iran policy concerning the frozen funds and perhaps even the military hardware.

A settlement can probably be reached without compromising U.S. relations with Arab Gulf states, which still may feel threatened by Iran's military forces.

This equipment technically is Iran's property, and a firm Iran-Iraq cease-fire probably means that Iran would pose less of a security threat to its neighbors.

This sensitive period for U.S.-Iranian relations comes at a crucial time in the U.S. presidential campaign. Both the Republican and the Democratic candidates should resist the temptation to use inflammatory rhetoric against Iran.

Idle words may appease domestic constituencies, but they do not serve our national interests well. At stake are the lives of nine American hostages, peace in a troubled region, and future relations with a key Middle East state.

(David S. Dodge, the first American to be taken hostage in Lebanon by forces supported by Iran, was kidnapped in July 1982 while he was acting president of the American University of Beirut; he was released one year later. Part of his captivity was spent in Iran.)