The Soviet government said in an authoritative comment yesterday that President Carter's speech last week on U.S.-Soviet relations contained words "which have a smell of the malicious spirit of the Cold War." The Kremlin warned it would not accept what is called "a series of ultimatum demands" from the United States for confrontation or cooperation.

The commentary, contained in the weekly authoritative international review of the Communist Party daily, Pravda, continues the sharp response the Soviets have made to Carter's speech on Wednesday. It reiterates the official line that the president's national security adviser, Zbigniew Brzezinski, is to blame for what the Kremlin views as the pugnacious tone of the presidential address.

"The Americans and European public are concerned by the fact that the basically aggressive, tough line of Brzezinski, who is widely known for his anti-communism, is getting the upper hand in the White House," stated the unsigned commentary. "The policy is not only fraught with the danger of a throwback to the Cold War . . . but harbors the danger of confrontation," asserted the newspaper.

In an address to the Naval Academy graduating class, the president declared that the United States is deeply concerned by Soviet military activities in Africa and elsewhere, and said bluntly that they were incompatible with the American view of detente. While underlining continued support for a new treaty with the Kremlin on limiting strategic weapons, Carter said, "The Soviet Union can choose either confrontation or cooperation. The United States is adequately prepared to meet either choice."

The Annapolis speech coincides with a fundamental review by the administration of its relations with the Kremlin, at a time when the two governments are taking an increasing negative view of each other.

The emerging Kremlin response underscores Soviet determination not to be seen as backing down from a challenge by the White House. The Soviets have sought to refute, point by point, each of the president's assertions about how easier relations that have grown between Moscow and Washington since the early 1960s are threatened by Soviet projections of power far from home as well as domestic policies of the Kremlin on human rights and other issues.

Pravda found part of the Annapolis speech to its liking. "There are some positive moments in the speech," it told readers. By his word [Carter] believes that detente between the U.S. and U.S.S.R. has fundamental significance for maintaining peace all over the world, that Washington has . . . readiness to study the possibility of cooperation with the U.S.S.R. in strategic arms limitation talks and a comprehensive test ban treaty and other matters.

"At the same time, these good words do not agree with the others, which have a smell of the malicious spirit of Cold War and . . . in the main, with the deeds of the U.S. administration.It is not by chance that most observers point out in this speech the hard tone and stress not on cooperation but on competition with the Soviet Union."

"In essence," Pravda said, "Carter's speech is a series of ultimatum demands to the U.S.S.R. But on what basis? Alas, not on the reason and detente basis -- principles fixed by the signature of the president under Helsinki and other Soviet-American documents of the first half of the 1970s."

The commentary told readers: "Not only did the U.S. president make impermissible outbursts against the social system in Soviet Union, but also demanded freedom of action for imperalist agents in the socialist countries and refusal by the U.S.S.R. and other socialist countries to support the national liberation movements in Africa and other continents. All this was accompanied by an unambiguous warning that in case of noncompliance on the part of the Soviet Union, the progress of detente will be evidently undermined."

The article then reiterated Soviet assertions that "it is not the U.S.S.R. or Cuba but the U.S. and its allies "that invaded Zaire and decried what it said was creation of "an invasion force for struggle against the national liberation movements . . . and turning NATO into a world gendarme of imperialism."

Calling Carter "the master of the White House," Pravda accused him of increasing NATO strength while Warsaw Pact countries have not increased their strength.