The Rev. Jesse L. Jackson opened the annual convention of Operation PUSH here today, calling for increased enforcement in the South of the "unfulfilled" Voting Rights Act. And a white Democrat from the North challenged his party's presidential contenders to put civil rights atop their agenda.

"It's long past time for my party, the Democratic Party, to end its silence in the '80s" on civil rights, said Sen. Joseph R. Biden Jr. (D-Del.) in a keynote address that elicited amens. "We cannot wait any longer because our soul will be corrupted by our silence. It is the only way the Democratic Party can . . . return to a state of grace."

Biden set the tone and agenda for the six declared Democratic presidential candidates who are scheduled to make pitches for black votes in political roundtable talks here Thursday night.

"They will speak to you of civil rights in Atlanta this week, but what will they say next week in Iowa?" asked Biden, ranking Democrat on the Senate Judiciary Committee, who has opposed school busing for integration.

The week-long convention of PUSH (People United to Save Humanity, Jackson's organization for social and economic activism) is being held while some Democratic Party strategists are arguing that an open competition for the votes of blacks, women and labor, the traditional backbone of the national Democratic Party, will drive conservative voters back to President Reagan in 1984, if he seeks reelection.

Jackson, who is pondering a run for the Democratic presidential nomination, told of voting discrimination against blacks that he has discovered traveling across the South in an effort to register 2 million blacks.

"Eighteen years later after passage of the Voting Rights Act , only 1 percent of the elected officials in the South are black," he said, citing many Georgia counties for unfair voting practices. Jackson also warned the Democratic Party to address its black constituency or risk losing it.

"We don't want to be the Harlem Globetrotters of the Democratic Party and provide the tricks and not have a say in the salary and the benefits," he said at a luncheon speech to PUSH delegates.

Civil rights lawyers later met to map strategies to challenge such voting rights barriers as runoff primaries in several southern states. These require candidates to achieve a majority or face a runoff and, according to Jackson, make it impossible for a black to be elected.

"It is the key impediment to voter registration," he said.

Paul Hancock, an attorney in the Civil Rights Division of the Justice Department, said that his agency is working hard to enforce the Voting Rights Act, adding, "We still have a long way to go. I don't mean to suggest that the problems in voting are over."

The department is expected to dispatch federal observers to monitor Aug. 2 primaries in Mississippi, one official said.

Jackson said that the convention will also tackle the dilemma of black colleges, black corporate affairs and foreign policy from South Africa to El Salvador.

Former vice president Walter F. Mondale, Sen. Alan Cranston (D-Calif.), Sen. Gary Hart (D-Colo.), Sen. Ernest F. Hollings (D-S.C.), Sen. John Glenn (D-Ohio) and former Florida governor Reubin Askew are due to address the convention Thursday. Chicago Mayor Harold Washington and Gov. James B. Hunt of North Carolina are also among the scheduled speakers.