A day after fiery anti-American demonstrations, President Clinton tried to smooth out a rocky visit to Greece today by acknowledging that the United States was misguided in backing a rightist military coup here 32 years ago.

Clinton assured an audience of business and community leaders that the United States values strong ties to Greece and offered a near-apology for the U.S. role during seven years of repressive dictatorship by a military junta that overthrew the country's leftist government in 1967.

"When the junta took over in 1967 here, the United States allowed its interests in prosecuting the Cold War to prevail over its interests--I should say its obligation--to support democracy, which was, after all, the cause for which we fought the Cold War," Clinton said. "It is important that we acknowledge that."

The audience erupted in applause, a measure of the deep feeling that remains from that era.

In the past two years, Clinton has offered several apologies or near-apologies for U.S. actions that occurred before his presidency. In Uganda in March 1998, he apologized for America's role in the slave trade and support of anti-communist dictators. A year later in Guatemala, he said the United States "was wrong" to have backed a regime that killed thousands of civilians during guerrilla conflict from 1960 to 1996.

Clinton has also expressed contrition for events that took place during his administration. He told a crowd in Rwanda in 1998 that the U.S. "did not act quickly enough after the killing began" to stop a brutal war between ethnic groups. The president has sometimes cited the Rwanda experience in defending the NATO bombing campaign against Yugoslavia this year.

Greek anger over that offensive, along with lingering animosity here about the American role in the 1967 coup, helped fuel Friday's protests. The Greek Communist Party helped organize the demonstration, in which thousands of people hurled stones and gasoline bombs at banks and police, but it blamed the violence on non-party anarchists.

Clinton's remarks about the coup were similar to those made before by Nicholas Burns, the U.S. ambassador to Greece. White House spokesman David Leavy told reporters, "This is not an apology. This is an affirmation of the president's views about supporting democracy."

In an interview, Greek Foreign Minister George Papandreou called Clinton's remarks "a very important statement. I think what Clinton was doing was turning the page on a part of our past that has fueled over the years these demonstrations and misunderstandings."

Clinton appeared eager to soothe Greek citizens, especially Athenians inconvenienced by his visit, which prompted police to shut down much of the city. He expressed awe at his first trip to the Acropolis and its crowning architectural glory, the Parthenon.

Later facing Greek reporters who devoted extensive coverage to his visit and the rampage it triggered, Clinton said: "I think that we have to--especially in Greece--reaffirm the right of people to protest in a democracy." But protests should be peaceful, he said, expressing sympathy for those "who had their property injured."

The government of Prime Minister Costas Simitis walked a careful line during the visit, basking in Clinton's compliments but wary of appearing to grant his every request. The Greeks, for example, declined to sign an agreement meant to crack down on terrorism, which the Clinton administration has urged them to do. Government spokesman Alex Rondos said Greece plans to sign the agreement, which calls for greater sharing of counter-terrorism expertise and information between the two nations, later this year.

Nevertheless, Simitis and other Greek officials joined Clinton in portraying the visit as a success.

"This visit does not just confirm the past," said Simitis, noting the legacy of U.S.-Greek friendship, it also "constitutes a guarantee for the future."

Much of the day's discussions concerned Greece's longtime rival, Turkey, and the two countries' disputes over Cyprus, a divided Mediterranean island country whose northern third is controlled by ethnic Turks. Only Turkey recognizes the northern part as a sovereign "Turkish Republic of Northern Cyprus."

At a joint news conference with Clinton, Simitis said his government will back Turkey's efforts to join the European Union only if Turkey meets "certain conditions," including supporting "substantive" talks on Cyprus set for next month in New York. Turkish Cypriots have agreed to the talks, but it is unclear whether they will accept a nation with separate communities on the island--envisioned by Clinton and others who have pushed for the discussions.

On his rainy tour of the Acropolis with daughter Chelsea this morning, Clinton showed perhaps too much sympathy for Greece's campaign to recover the Elgin Marbles--a collection of 17 statues and part of a 160-yard frieze taken from the Parthenon by Britain's Lord Elgin in the early 19th century. Greece contends that the marbles, now housed in the British Museum in London, were stolen; Britain maintains that Elgin acquired the sculptures legally.

Greek Minister of Culture Elizabeth Papazoe said Clinton told her that he thought all such items from the world's museums should be returned to their original sites.

"Oh no, that's the opposite of what we want!" Papazoe said she told the president, envisioning the havoc that such a widespread policy would cause for museums.

She said the president told her he would speak with British Prime Minister Tony Blair about the marbles on Sunday in Florence, where they and several other world leaders will attend a conference.

CAPTION: President Clinton escorts daughter Chelsea at the Parthenon, where he supported reclaiming sculptures from Britain.

CAPTION: A Greek youth looks through a bank's shattered window after anti-American demonstrators rioted in central Athens.