President Carter steered his way along a road of invective that has already become well-rutted in this young fall campaign, suggesting today to an all-black audience that Ronald Reagan had injected hatred and racism into the contest by using "code words like 'states' rights."

In the Atlanta church where the Rev. Martin Luther King Sr. preached for years, Carter cautioned his audience that if the Republican is elected, there probably will never be a national holiday in memory of King's slain son.

The president also said in the text of his speech that Reagan had opposed the 1964 Civil Rights Act. The president omitted this as he free-wheeled through the speech, ignoring his text, but aides say he stands behind it.

Interestingly, White House press secretary Jody Powell said there is no record of whether Carter himself supported the Civil Rights Act in 1964, when he was a freshman state senator in Georgia. Powell said he does not know whether Carter ever spoke out publicly in favor of the bill, but said Carter did actively support Lyndon Johnson, the bill's chief advocate, for president that year.

Reagan, campaigning in Texas, responded that "there were a great many people who questioned some things" in the law. Later, he went on the offensive, saying in a news conference that Carter's attack was "shameful." [Details on Page A3.]

As he wound up his two-day campaign swing, Carter sought to keep the pressure on. His early campaign pattern features hard-hitting attacks, often opting for the most extreme public interpretation of Reagan's record on controversial issues.

Reagan has done much the same, including a campaign-opening statement that reached to link Carter with the Ku Klux Klan. Reagan has since regretted this, since it mostly provided the president with campaign fodder that he has used frequently throughout the South.

The result has been a presidential campaign that looks vice presidential, with all participants striving for the all-out attack that traditionally was reserved for vice presidential candidates only -- Spiro Agnew, 1972; Bob Dole, 1976 -- as presidential candidates sought a somewhat loftier tone.

The campaign tones of 1980 have been decidedly shrill. And today, Carter continued to perform in that voice. Referring to previous Reagan campaign comments, the president said:

"You've seen in this campaign the stirrings of hate and the rebirth of code words like 'states' rights' in a speech in Mississippi; in a campaign reference to the Ku Klux Klan relating to the South. That is a message that creates a cloud on the political horizon. Hatred has no place in this country."

In a recent appearance at the Nashoba County Fair in Mississippi -- the country where three white civil rights workers from the North were murdered in the 1960s -- Reagan indeed said he favored "states' rights." The phrase was a code word for resistance to desegregation in the 1960s.

Press secretary Powell said the president was referring to that comment by Reagan. And, when told that a Reagan spokesman said the Republican nominee now favors the 1964 Civil Rights Act that he once opposed, and in fact would like to make it stronger, Powell suggested that Reagan try another tack. He urged that Reagan come out in favor of the fair housing bill, which he said is now being blocked by conservatives in the Senate after being approved by the House.

Carter also continued his squeeze on Reagan's Ku Klux Klan gaffe, in which the Republican nominee derided Carter for opening his campaign in the Alabama city that Reagan labeled the birthplace of the KKK.

Standing on the steps of the Ebenezer Baptist Church in Atlanta, Carter told reporters: "Obviously the Ku Klux Klan is an obnoxious blight on the American scene and anyone who injected it into the campaign made a serious mistake."

Reagan was the first candidate to refer to the Klan, but before him, Carter's own secretary of Health and Human Services, Patricia Harris, had injected the KKK into the campaign. She said the Reagan candidacy raised the "spectre of white sheets" because the klan had endorsed Reagan and highly praised his Republican platform -- an endorsement Reagan promptly repudiated. Andrew Young had also written a newspaper column noting angrily the KKK endorsement of Reagan and his party's platform.

Today, the issue was injected anew, as Carter sat on the stage alongside Young, the elder King and Coretta King, widow of the slain rights leader. Rep. Parren Mitchell (D-Md.) told the audience of Southern black political activists that he would address them in greater detail as soon as the president left and promised:

"I'm going to talk about a man who has embraced a platform that some men known as the Ku Klux Klan said couldn't be better if they'd written it themselves . . . who seeks the presidency of the United States with the endorsement of the Ku Klux Klan."

Carter looked momentarily uncomfortable, yet he grinned and shook Mitchell's hand when the congressman had finished. And when Carter got to the microphone he said, "I wish I could sit in on the speeches after I leave -- because there are some things that are going to be said that I would really like to hear. But I'll depend on you all to give me a report."

As he campaigned in Atlanta, the South Carolina mill town of Startex, and in Cleveland, Carter continued to charge that Reagan has been "muzzled" by aides because of recent miscues.