The Rev. Jesse Jackson, testing the waters for a black presidential candidacy down South, today became the first black man since Reconstruction to address a joint session of the Alabama Legislature, where his rousing message of racial conciliation and economic recovery was warmly received.

A rapt audience of state legislators, most of them white, and black supporters in the packed chambers interrupted the civil rights leader 12 times with applause. White lawmakers especially warmed to his attacks on foreign nations for "unfair trade" practices that have cost this hard-hit state of steel mills and rubber plants thousands of jobs.

At times, Jackson even echoed his former arch enemy, Gov. George C. Wallace; as he railed at "Honda and Toyota, Suzuki and Yamaha, Sony and Panasonic, being unloaded at the docks and replacing Buick and Chrysler in the American market."

It was a moderate, mainstream Jesse Jackson preaching a new "politics of soul" to a new South.

"We put too much focus on the schoolyard and not enough on the shipyard," said Jackson, who is stumping the South on a massive voter registration drive which he hopes will sign up 3 million unregistered black voters.

"He makes some good points about our economy," said state representative Charles Adams, 49, a white, self-styled conservative who labeled the speech "very inspirational."

"It's about time we forgot about black and white and started talking about employed and unemployed."

"It wasn't a racist type speech at all," agreed J.E. Turner, 46, a white legislator from Mobile. "It was very appropriate."

It was a day full of symbolism for a black leader who dodged police dogs and clubs here 17 years ago on the bloody march from Selma to Montgomery with the Rev. Martin Luther King Jr., the slain civil rights leader. Jackson stood near the spot in the Alabama Capitol where Jefferson Davis was sworn in as president of the Confederacy.

"This has been a marvelous place to speak, where Jeff Davis spoke and Martin Luther King Jr. should have spoke," he said. "Perhaps he was too close for you to see. But he did say we'd learn to live together [and] . . . move from the battleground to common ground to higher ground."

His voice rising and falling, sweating profusely, Jackson turned the chamber into a tent revial for coalition politics in a state where the black vote played a crucial role in electing Wallace to a fourth term.

In an interview, Jackson called the South the key to a "black-progressive white coalition" that will figure heavily in the Democratic nomination and the attempt to defeat President Reagan. Blacks are 19 percent to 35 percent of the population in seven southern states where Reagan beat Carter by narrow margins, he said.

The majority of the 3 million unregistered black voters in the South are in those states, he said; and that's where he aims to mobilize clergy, local politicians and disc jockeys to inspire blacks to register. Alabama was his 'third stop after North Carolina and Georgia.

A resolution to invite Jackson passed by voice vote last week. Black state representative Alvin Holmes, the floor leader for the Alabama Education Association, one of the state's most powerful lobbies, pushed it through and there was little dissent.

"Political power talks," said Holmes, one of 17 blacks among 105 legislators.

Not every white legislator appeared to be thrilled, however.

"When in Rome, you do as the Romans do," said white representative Harrell Blakeney, 62, a former National Guard officer who last saw Jackson, the protester, on the front lines of the Selma to Montgomery march in 1965.

But he added: "Time is one of the best healers there is. There's been a lot of changes in all of us in the last 18 years."

Jackson played down talk of his possible presidential candidacy, saying he will decide possibly "sometime in August" whether to run. But he acted like every other Democratic who has come courting Alabama.

He met with newspaper editorial boards. He courted Wallace.

A long-time foe, Wallace graciously received Jackson, who tried, but failed, to rally, enough blacks to defeat the governor during his campaign for last fall. On Monday, he served Jackson pecan rolls on silver trays and iced tea in silver pitchers on the sun porch of the mansion.

"Jesse, you're running for president, huh?" said Wallace, according to a tape of the meeting obtained by The Washington Post. "I ran one time, you know. It's a real tough thing running for president. You see what happened to me."

Wallace has been confined to a wheelchair since an assassination attempt left him paralyzed from the waist down during his 1972 presidential bid. He is recovering from a long illness.

For Jackson, it was a "summit meeting," the "end of a no-talk policy." He praised Wallace as a man of "charisma, stature and grace," then he asked him to sign a bill providing more voting registrars and registration of high school seniors on graduation day.

Later, at the Lilly Baptist Church, Jackson preached registration to 1,500 blacks, warning youths to vote or to contract "political herpes."

He coaxed the unregistered to come forward for their political baptism. Two dozen came forward to applause. One registrar said she signed up 150 new voters before the last sermon, among them George Smith, 24 an unemployed bricklayer who hasn't worked steadily in three years.

"It never seemed worth registering before Smith said. "But tonight, I just decided to do it. I might as well vote. It might count one day."