Secretary of State George P. Shultz, declaring that the turmoil in South Africa has taken a "sharp turn for the worse," pleaded with a broad coalition of senators yesterday not to limit U.S. flexibility by legislating new sanctions against the Pretoria regime.

Shultz ran into a storm of protest, some of it highly emotional, from a Foreign Relations Committee that was almost unanimously critical the day after a policy statement on South Africa by President Reagan.

The tenor of the hearing and a statement by Senate Majority Leader Robert J. Dole (R-Kan.) strongly suggested that the Senate will join the House in voting punitive sanctions despite objections by Reagan and Shultz. Sen. Richard G. Lugar (R-Ind.), chairman of the Foreign Relations Committee, said there is a bipartisan majority in the Senate for voting new anti-Pretoria measures, but no agreement yet on which ones to adopt.

Sens. Edward M. Kennedy (D-Mass.) and Lowell P. Weicker Jr. (R-Conn.) said late yesterday they will seek to attach sanctions legislation to the bill raising the ceiling on the national debt, the pending business in the Senate. Weicker said that "the time to choose is hours away."

A spokesman for Lugar said the Foreign Relations Committee hopes to clear a sanctions bill for floor action next week, with the aim of final passage before the mid-August congressional recess.

Shultz, in the most extensive and pessimistic administration assessment yet of the turmoil in South Africa, spoke of "narrowing odds" that "an impending tragedy" can be prevented. In the past few months, he said, "Slender hopes for peace and reconciliation have fallen victim to a headlong rush toward violence. Doors that need to be open have slammed shut. Forces of political fragmentation and racial polarization have been set loose. They will be very difficult to contain."

Saying that the forces of the marketplace have already imposed strong sanctions against South Africa, Shultz painted a grim picture of capital flight, voluntary disinvestment and disengagement by U.S. and other foreign corporations, emigration by whites, massive unemployment among urban blacks and rising violence and terrorism "from extremists on all sides." All this, Shultz said, is "eroding the capacity of any future South African government to address the country's problems."

The "downward slide" of South Africa threatens the entire southern Africa region of a dozen states and 150 million people, Shultz declared. He said U.S. efforts to deal with the economic crisis in Africa are hurt by congressional reductions in foreign aid, which he said is being "cut to ribbons."

Before delivering his lengthy statement, Shultz was required to listen as 10 senators of both parties, a majority of the 17-member committee, spoke one after the other in disappointment with or opposition to Reagan's speech or otherwise separated themselves from administration policy.

Sen. Joseph R. Biden Jr. (D-Del.), in a fiery exchange, accused Shultz of "refusing to act on a morally abhorrent point" by failing to do anything specific against apartheid and said "I'm ashamed of the lack of moral backbone to this policy."

Shultz angrily replied, "I resent that deeply because there is a tremendous moral backbone in that policy on a bipartisan basis" and charged Biden with "calling for violence" in his remarks about the travail of South African blacks.

At another emotion-laden point, Kennedy called the administration policy of "constructive engagement" in South Africa "an unmitigated disaster" and declared that Reagan "doesn't speak for the United States . . . doesn't speak for the American people" on the South Africa issue.

Sen. Nancy Landon Kassebaum (R-Kan.), chairman of the Africa subcommittee, said she was "deeply disappointed" in Reagan's speech because it contained "no renewed vigor" in the effort against apartheid. Saying that Reagan is the one person who could convince South Africa's white leaders that they must change course, Kassebaum said that he should speak to them frankly as "a true friend."

During the 3 1/2-hour hearing, only Sen. Larry Pressler (R-S.D.) spoke in agreement with administration policy against new sanctions, and most lawmakers made it clear they were ready to vote for such measures.

Shultz, while arguing against legislated sanctions, left the door open for the administration to take anti-Pretoria measures of its own in consultation with other nations.

"We are prepared to take actions, with our allies, to change the mix of our pressures -- positive and negative -- to meet the rapidly changing course of events in South Africa," declared Shultz. He went on to call for "maximum flexibility," including generous grants of presidential discretion to impose or lift sanctions as necessary. "We cannot afford to be locked in the straitjacket of rigid legislation, no matter how well intended or carefully drafted to anticipate events that may or may not occur," Shultz said.

Shultz suggested that administration-initiated measures might come in September, saying that is when a U.S. review as well as "international consultations" on South Africa are expected to conclude.

As part of its diplomacy, Shultz announced, the administration intends to raise the level and frequency of its contacts with black opposition groups in South Africa, including the outlawed African National Congress. Shultz said there are "serious questions" about ANC objectives, tactics and communist influence in its inner circle, but that there is "a compelling need" for discussions with this group.

Shultz said he is willing to meet ANC leader Oliver Tambo, who conferred last month with the British government, but that no date has been set for such a meeting.