American Ambassador Arthur Hartman today received a chilly response when he called on Soviet Foreign Minister Andrei Gromyko to give advance notice of President Reagan's program of economic sanctions against the Soviet Union.

In a meeting that lasted almost an hour, Gromyko was said to have rejected angrily American contentions that the Kremlin was responsible for the military crackdown in Poland. Gromyko instead accused the United States of interfering in internal Polish affairs and said such activities should be halted.

Despite more than 12 hours notice, the Kremlin had no immediate comment on the American sanctions, which were not reported by the official news agency Tass.

But, in a move reflecting Soviet anger, Tass departed from its normally scrupulous observance of diplomatic protocol to report the subject of the conversation between Gromyko and Hartman.

"Since the U.S. ambassador raised the question of the situation in Poland," Tass said, "he was told that the U.S. government should put an end to interference in the internal affairs of a sovereign state, the Polish People's Republic, which has been continuing in various forms, overt and covert, for a long time now."

Gromyko also described the military takeover in Poland as a purely internal Polish matter. Tass quoted him as saying that "the measures taken by the Polish leadership to normalize and stabilize the situation in the country are a matter of the Poles themselves and them alone."

Western diplomatic observers here said the U.S. sanctions appear to be largely symbolic and unlikely to cause any particular economic difficulties for the Russians.

Since former president Carter instituted economic reprisals following the Soviet invasion of Afghanistan in December 1979, Soviet-American exchanges in virtually all areas have been drastically curtailed. Short of a new grain embargo, the United States has little economic leverage on Moscow without support of other Western countries.

Reagan, however, lifted Carter's partial grain embargo and last fall negotiated a new deal with the Russians that provides for record levels of U.S. grain to be available to the Soviet Union until next September.

Reagan had earlier announced a series of economic sanctions against the Polish military government. So far, however, other Western nations have not followed the U.S. lead in imposing sanctions.

The Russians, however, are believed to be concerned about the political impact of Reagan's action. Western diplomatic sources said the NATO allies already are divided in their attitude toward the Polish government, and there was little enthusiasm among Western Europeans for striking directly at Soviet interests at this time.

In a propaganda campaign that is likely to become more intense in the coming days, the Soviet Union has stressed the unpredictability and bellicosity of the Reagan administration in contrast to other Western nations.

These charges depict American foreign policy as turning progressively more risky for Europeans and jeopardizing the political and economic gains of a decade of detente.

The suspension of U.S. licenses for equipment to be used in the construction of a gas pipeline from the Urals to Western Europe was expected to be met by objections in Western Europe. American businessmen here quoted Soviet officials as saying similar equipment could be obtained in West Germany and Japan.

The West Germans are interested particularly in the pipeline, and Chancellor Helmut Schmidt last summer rejected a personal appeal by Reagan that the Germans abandon the project.

There is also the expectation here that the European nations will resist Reagan's push for the suspension of high-technology exports to the Soviet Union. In the wake of Carter's sanctions, trade relations expanded considerably between major Western European nations and the Soviet Union.