The Carter administration issued its strongest warning yesterday against Communist participation in any Western European government, in an attempt to shore up Italy's tottering Christian Democrat rule.

An Italian Communist leader at the same time forecast "the imminent resignation" of the government of Premier Giulio Andreotti. Political sources in Rome said Andreotti may resign by Monday rather than accept Communist demands for a coalition with his Christian Democrat Party.

Until now, the Carter administration had avoided officially declaring explicit opposition to Communist participation in any Western European government, on grounds that it could only evoke Communist charges of foreign interference in domestic affairs.

Yesterday the Carter administration said, "Our position is clear: we do not favor such participation and would like to see Communist influence in any Western European country reduced.

That went doubly further than the administration has gone before, in outright opposition to Communist participation and in the call for reduction of "Communist influence."

President Carter in the past has often used such language as "we prefer theat the governments involved continue to be democratic and that no totalitarian elements become either influential or dominant." Carter also has sometimes said that he hopes Communist success "will be minimal." But he always has stressed that foreign voters must make "their own decisions" and that the United States will not interfere.

"There has been no change in the administration's attitude toward Western European Communist parties," the administration maintained in the new statement, issued by the State Department.

However, the statement said, "recent developments in Italy have increased the level of our concern."

The U.S. position remains, the administration said, that the decision on how West European nations are governed "rests with their citizens alone"

"At the same time," the statement said, in rationalizing the stronger declaration, "we believe we have an obligation to our friends and allies to express our views clearly."

It went on. "The United States and Italy share profound democratic values and interests, and we do not believe that the Communists share those values and interests."

The statement added, as President Carter said last week in Paris, where French Communists also are pressing for a share in governmental rule: "It is precisely when democracy is up against difficult challenges that its leaders must show firmness in resisting the temptation of finding solutions in non-democratic forces."

When it came to office, the Carter administration decided it would do more harm than good to maintain the policy of dire warning against "eurocummunism" which was followed by Secretary of State Henry A. Kissinger in the Nixon and Ford Administration.

Kissinger and Ford, out of office, both maintain that the milder approach is ineffectual. In a broadcast to be aired tonight by NBC News, Kissinger forecasts "grave consequences for the entire West" if Italy's "slide toward communism" continues.

The Carter administration's new language, considerably short of that, resulted from a White House meeting Wednesday with Richard N. Gardner, U.S. ambassador to Italy.

Gardner, who had been using a low-keyed, private diplomacy approach to the issue of Communist participation in the government, reportedly sought stronger presidential authority. Although there have been mixed views among administration officials about precisely how strongly the United States should speak out at this near-crisis point in Italian politics, an official said yesterday that these views were in a narrow range and "there is no division in the government."

Some officials said privately yesterday that a major factor behind the new statement on communism is that, whatever happens inside Italy, the Carter administration wanted to be on the record with a firmer statement, to avoid being accused of "fiddling while Rome burns," if the Communists do enter the government.

In the past the United States has contributed covert funds to the Christian Democrat Party during its 32 years of rule. State Department spokesman John H. Trattner told a reporter yesterday who asked if that might be repeated. "We do not intend to get involved in the way you suggest."

The statement issued yesterday, Trattner maintained, does not represent any interference in Italy's domestic affairs. Communists have charged the Gardner's recall to Washington for consultations itself amounted to interference.

Italy's Communist Party, the strongest in Western Europe, seeks political power equal to the one-third of the vote it won in the 1976 elections. This was only 3 per cent behind the Christian Democrats, who rule as a minority government.

If there is a new election, many political specialists forecast that both the Communists and Christian Democrats would gain votes, ending either with Communists in government or civil warfare. Italy is now experiencing widespread violence and severe economic strain.

A Christian Democrat deputy, Guido Bodrato, said yesterday in Rome that efforts will be made to find a compromise to avoid forcing an early, hazardous election.