The State Department yesterday asked Ernest W. Lefever, President Reagan's controversial nominee as assistant secretary of state for human rights, to cancel his scheduled Sunday appearance on "Meet the Press," signaling the end of a two-day-old counterattack on his critics.

Department sources said Lefever was told that such an appearance the day before the Senate Foreign Relations Committee resumes its confirmation hearing on his nomination would be counterproductive.

Lefever also canceled a scheduled Saturday night speech before the National Confederation of American Ethnic Groups.

One State Department source said the department did not want "to create any appearance of trying to influence the Senate Foreign Relations Committee."

Another said that Richard Fairbanks, assistant secretary of state for congressional relations, feared that Lefever's combative public assetions that his opponents are "Marxists" or "Marxist-oriented" critics who were really attacking the president and the administration's foreign policy were backfiring.

This brought Lefever into several testy exchanges with members of the committee, including Chairman Charles H. Percy (R-Ill.), during hearings last week.

According to a "Meet the Press" aide, Lefever called yesterday to withdraw after having agreed to the appearance several days ago.

Lefever has appeared on the "Today show and WRC radio in the past two days. The appearances were his own initiative and the State Department was not consulted on them, department sources said.