Iranian Finance Minister Abol Hassan Bani-Sadr, the radical economist who favors a quick solution to the U.S. hostage crisis, took a strong early lead today in the nation's first presidential election, according to unofficial Interior Ministry estimates.

Heavy voter turnout was reported in most parts of the country.

Ministry officials said Bani-Sadr, 47, appeared to be winning 70 to 80 percent of the vote in many areas. The French-trained economist was the preelection favorite.

Although Bani-Sadr claimed victory shortly after the polls closed last night, no concessions of defeat were heard from his two chief rivals -- former naval commander Ahmad Madani, the favorite of the middle class, and Hassan Habibi, the clergy-backed candidate.

Interior Ministry officials said that Madani was taking second place in the balloting and that Habibi was running third.

If no single candidate emerges with a majority of the vote, a runoff will be held Feb. 8. Election officials said today they may not have a final tally until Tuesday because of the large number of candidates in the race -- 66 by last count.

Bani-Sadr, who served briefly as foreign minister after Islamic militants seized the U.S. Embassy in Tehran 12 weeks ago, has long advocated a fast decision to release or punish the estimated 50 Americans being held hostage.

In an interview with the Reuter news agency last night, he said he would "try to bring this problem between the Americans and ourselves to an end in a way which safeguards the demands and the independence of Iran."

Despite Bani-Sadr's statements, the new president will be constitutionally subordinate in power to Ayatollah Ruhollah Khomeini, who as the nation's top theologian, can dismiss the constitution, Khomeini also has greater authority over the armed forces and the law.

The 79-year-old spiritual leader was said to have voted early yesterday morning at a Tehran hospital where he is receiving treatment for a heart ailment. Khomeini endorsed none of the candidates.

The significance of a Bani-Sadr victory, however, has already been calculated in New York, where sources said U.N. Secretary General Kurt Waldheim feels he has the finance minister's approval to go ahead with a U.N.-sponsored investigation of "crimes" of the deposed shah, presumably in exchange for release of the hostages.

Early in the crisis it was Bani-Sadr's interest in a U.N.-sponsored solution that cost him his foreign policy job. As the crisis has stretched on, however, and fear has grown over the Soviet invasion of neighboring Afghanistan, many believe the Iranian position has softened at least to the extent that such a solution would be considered.

Although the emotional hostage crisis has clearly been a factor in Iran's first presidential contest after 2,500 years of monarchy it was just one of numerous issues that drew millions to the polls yesterday in one of the coldest days of the winter.

Khomeini had made a dramatic sickbed plea for voter turnout Thursday. He was said by doctors to be in generally "good condition" yesterday, although he complained of chest pains for about 20 minutes in the early morning.

Responding to his appeal, long lines of voters accumulated outside makeshift polling places at mosques, schools and warehouses as election authorities advised iliterate persons to "find someone you can trust" to fill in the write-in ballots, according to reports.

Except for minor scuffles among supporters of rival candidates in the Caspian Sea town of Rasht and the southern oil city of Ahwaz, as well as scattered clashes in the Kurdish region of western Iran, there were no reports of violence before polls closed at 6 p.m. local time.

Although Kurdish rebels made good on their threat to boycott the elections because their favorite candidate was disqualified last week, Azerbaijani, Baluchi and Turkoman minority groups were reported to be voting.

The election has been considered an important test of autonomy movements in Iran's provinces, where religious and ethnic minorities have staged fierce antigovernment rallies and fought Khomeini loyalists in past weeks -- posing an important threat to central control.

Although the nation's electorate of 22 million was given the chance to vote for the establishment of an Islamic Republic and the enactment of a new constitution, yesterday's contest provided the first opportunity for Iranians to voice a preference for the style of their national leadership.

Faced with an original list of more than 100 contenders, Khomeini waived his constitutional right to screen candidates, urging all Iranians over 16 years of age to sort through the qualifications themselves in choosing their first president.

Although the precise powers of office will depend on who executes them, the man who fills Iran's highest elected office for the next four years will have the authority to nominate the prime minister and sign treaties.

The list of candidates included politicians who have been influential since last February's revolution, including Foreign Minister Sadegh Ghotbzadeh, right-wing nationalist Dariush Forouhar and former government spokesman Sadegh Tabatabai.

But the contest quickly came down to a race between Bani-Sadr and Madani, the 51-year-old former naval commander and recently resigned governor general of oil-rich Khuzestan, who earned a reputation as a strongman for quelling Arab unrest in his southern province.

Another contender, Habibi, the spokesman for Iran's ruling Revolutionary Council, emerged as a serious rival after the candidate of the clergy and powerful Islamic Republican Party dropped out and Habibi picked up some of his support.

The campaign had many of the trappings of an American election race with candidates plastering the walls of Tehran with posters and handing out literature in the streets and shopping centers. Clearly the most energetic candidate, Bani-Sadr criss-crossed the nation in search of votes, drawing the greatest enthusiasm in poor sections of the country where residents were attracted to his economic views and his appeal to nationalism.