WASHINGTON, Nov. 25— Many European leaders applauded today's ruling against the former dictator of Chile, Augusto Pinochet, but within the United States Government and in some legal circles, there was a note of consternation at the potential power of a Spanish judge to transcend national borders in the name of international law.
Muted responses from United States officials reflected some uneasiness in Washington with the idea that former Government leaders can be held responsible by foreign courts. At the State Department and the National Security Council, spokesmen said that Mr. Pinochet's fate was a matter for the Spanish and British courts.
Alfred Rubin, a professor of international law at the Fletcher School of Law and Diplomacy in Boston, said the power of the Spanish judge in the case to reach across national boundaries was troubling.
''What's to prevent Spain from extraditing Henry Kissinger, who was involved in the coup?'' he asked. ''What's to prevent Spain from ruling the world? The whole thing seems to be leading to chaos, with every country sitting in judgment of the revolutions of other countries. That strikes me as undemocratic.''
Across Europe, many officials were openly elated.
In Geneva, Mary Robinson, the United Nations High Commissioner for Human Rights, said the ruling ''will hearten human-rights defenders around the world.'' The decision ''confirmed the emerging international consensus against impunity,'' said Ms. Robinson, a former President of Ireland.
In Paris, Jacques Chirac, the President of France, said: ''May justice be done, and may light be fully shed on Pinochet's responsibilities.'' The French Prime Minister, Lionel Jospin, said: ''It's a surprise, it's a joy, it's bad news for dictators.''
France, along with Spain, Belgium and Switzerland, has sought Mr. Pinochet's extradition for crimes against their citizens. The United States has not.
The German Justice Minister, Hertha Daubler-Gmelin, has said she would support an extradition request if there was evidence of damage suffered by German citizens. The German Greens Party, junior partner in the Government, praised the ruling. ''This confirmation of human rights from the motherland of democracy clears the way for legal proceedings against a criminal dictator to take their course'' in Spain, a ''democracy which is still young,'' said the party's co-leader, Gunda Roestel.
In the United States, relatives of victims praised the ruling. Michael Moffitt, whose wife of 113 days, Ronni Moffitt, was killed by General Pinochet's secret police, said the ruling was a ''great vindication.'' Ms. Moffitt died along with a former Chilean Foreign Minister, Orlando Letelier, when their car was blown up by a bomb in Washington in 1976.
''It's a great Thanksgiving Day present for a lot of people, a lot of victims of that beast,'' said Mr. Moffitt, 47, a financial manager living in New Jersey. More than 3,000 people were killed as the general took power in a 1973 coup. The dead included Charles E. Horman, a 31-year-old American working as a filmmaker and writer in Chile.
Today his mother, Elizabeth Horman, said the ruling gave her a measure of happiness. ''The wheels of justice grind slowly but they grind exceedingly small,'' said Mrs. Horman, an artist who lives in Manhattan and is in her 90's.
''I want Pinochet in prison,'' she said. ''Do you realize what he did to us? Do you know what kind of man my son was? He was attractive and humorous and loving. And he was a human rights advocate. And that's why he got caught up in the coup.''
Michael Ratner, director of the Center for Constitutional Rights, which represents Mr. Horman's family, said the Letelier and Moffitt killings represented strong legal cases against the former dictator. But he added that it was far from certain that the Justice Department would move against Mr. Pinochet.
Though mid-level officials at the Justice Department have discussed extraditing Mr. Pinochet in those killings, they have considered it as an option only if the former dictator won immunity from the British courts. Any extradition proceeding by the United States would have to be approved by the State Department and the White House.
In Madrid, Isabel Allende, the daughter of Salvador Allende, the elected president of Chile who overthrown by General Pinochet's coup, said: ''Future dictators will have to think very hard before they turn to killing, before they betray their oaths, before they break their democratic constitutions.''
She added: ''This is not a case of revenge. What we want is justice. We are fighting for justice and not impunity. I feel great satisfaction and it is a great, historical moment.''

Or as it is sometimes put,  "The mills of the gods grind slowly, but they grind exceeding fine."