Democratic presidential hopefuls strutted their New Moderation before the New South at a gala party fund-raiser here today, with former vice president Walter F. Mondale making an impassioned plea for black support and putting distance between himself and former president Jimmy Carter's talks this week with the Palestine Liberation Organization.

The importance of the delegate-rich South brought six of the Democratic party's seven White House aspirants out for the state's annual Jefferson-Jackson Day dinner as a new poll showed Mondale and Sen. John Glenn (Ohio) running about even against President Reagan in a presidential matchup in nine southern states.

Mondale, under fire from blacks since campaigning against Rep. Harold Washington in the Chicago Democratic mayoral primary, reminded Georgia's black caucus before the dinner that he had been at the fore of their civil rights struggle for two decades.

"We were together in every single fight . . . . I was involved emotionally . . . . I was perhaps the key person--intensely emotionally involved," said Mondale, his voice rising with emotion as the Rev. Martin Luther King Sr. interrupted with repeated "amens."

"I'm surprised sometimes at how a record gets forgotten," Mondale added. "I think everyone who's been involved knows I'm telling the truth."

Later at a news conference, Mondale was asked if he supported Carter's current diplomatic foray, as a private citizen, to the Middle East, where the former president said that he talked to the PLO.

Mondale responded that he did not know the details of what Carter had done. But he added that, "Our position in government was that . . . we would not have contact with the PLO. I would do that in private life as well."

Meanwhile, another former member of the Carter administration, Georgia Democratic Party Chairman Bert Lance, described the dinner as the most successful in party history, and said it raised more than $200,000. About 2,500 party faithful were at the cavernous World Congress Center downtown to see if the candidates were wearing enough conservative, or at least moderate, stripes.

"The South has an opportunity to exercise a kind of discipline on a Democratic candidate it has not had before," Lance said. "Candidates are going to have to be very specific this time and campaign as aggressively down South as they do in Iowa and New Hampshire."

After a candlelight buffet of roast beef and chicken, Glenn praised the South as the political "mainstream" of America, calling it a "lesson our party cannot forget," as he debuted in the South alongside five other Democratic contenders.

Glenn, describing what he admired in Georgia, put Atlanta Mayor Andrew Young first for securing the southern black vote for Jimmy Carter. "The party of Andy Young knows that black America doesn't want photo opportunities, but . . . equal opportunity," Glenn said.

Mondale evoked the strongest applause. Speaking last, he said, "In this century, I don't believe we've had a president more insensitive and more uncaring and more indifferent . . . than Ronald Reagan." Former Florida governor Reubin Askew hailed colleagues on the podium as good "vice presidential timber," while Sen. Dale Bumpers (Ark.) argued that a "burgeoning economy" could not "change the fact that James Watt is secretary of the interior or that this administration has a mindset that nuclear war is winnable."

Sen. Ernest F. Hollings (S.C.) warned Democrats to heed lessons from other failed economies, saying "England continues to go to hell in an economic handbasket tonight."

Sen. Gary Hart (Colo.) attacked the president, saying, "It's not enough to be a decent person, you must govern with decency."

Sen. Alan Cranston (Calif.) was represented by his son, Kim, who said, "California has so far produced three presidents: Herbert Hoover, Richard Nixon and Ronald Reagan, and we can do better."

Because of population growth in the Sun Belt and the Democratic Party's delegate allocation formula, which rewards the southern states for Carter's relatively good showings there in 1976 and 1980, the South has increased clout with more delegates to the national convention than ever. Party leaders say they plan to use it to bring Democratic contenders back to the middle of the road.

"What we're watching in Georgia and other southern states is to see if Mondale is moving to the middle from the left. If he can shake his '60s perception as a liberal, he's got a real good shot," said Paul Weston, state party executive director. "Otherwise, Glenn has the best chance. It will take a centrist to beat Reagan."

At stake are 1,046 delegate votes at the 1984 Democratic National Convention from 13 southern states--more than any other region in the country and more than 25 percent of the total of 3,923 delegates.

Tonight's candidate pilgrimage came almost one year before crucial early southern primaries in Florida, Georgia, Alabama, South Carolina, Mississippi and Arkansas. Only Iowa and New Hampshire precede that southern primary week.

Mondale was not the only one to meet with blacks. Bumpers called on Mayor Young, as did Hart. Askew was scheduled to lunch Wednesday with members of the Voter Education Project, which conducts black voter registration drives.

Claibourne Darden's poll of 1,000 voters in nine southern states showed Reagan vulnerable to Mondale and Glenn, with both pulling even with Reagan after trailing by seven points last fall. In October, Reagan led Mondale by 51.3 percent to 44.4 percent and led Glenn by 48.7 percent to 41.7 percent. In late February, Mondale and Reagan were tied at about 48 percent each while Glenn led the president 48.8 percent to 45.3 percent, which is barely within the 3 percent statistical margin of error.

Glenn had the highest approval rating of the five Democratic hopefuls measured in the poll, with 59 percent, compared with 48.2 percent for Mondale, 42.3 percent for Askew, 37.7 for Hollings and 34.7 for Hart.