Blacks may ''look beyond presidential elections'' in 1984 and concentrate instead on America's big cities, where black mayors could become the ''new breed'' of leaders rising on the political horizon, say civil-rights and black political leaders.
''We are looking beyond the presidential elections to find out whether black politicians can develop grass-roots power in cities and counties,'' says John E. Jacob, president of the National Urban League. ''This is an election year, and blacks can't afford to sit this one out because they don't like the presidential candidates. Other offices are up for grabs, and blacks are running for them.''
The National Urban League will concentrate on black political strategy for the election year at its 74th national convention beginning Sunday in Cleveland, Mr. Jacob says.
''Political decisions often determine what happens to issues black people consider critical - the black family, public school education,'' he adds.
Jacob also says former presidential candidate Jesse Jackson sparked a new awareness among blacks of the power of the ballot. The Rev. Mr. Jackson and five minority mayors are expected to speak out for a new brand of political activity in the South, and even in suburbia, at the Urban League convention.
The black electorate is ''a sleeping giant,'' says Tom Cavanagh of the Joint Center for Political Studies, a black ''think tank'' based in Washington.
''Elected black officials increased by 8 percent in 1982. A similar increase can be achieved in November if black voters continue the momentum developed from Jesse Jackson's campaign for president,'' he says.
Mr. Cavanagh says four new black congressmen could be elected this fall - Robert Clark in Mississippi, Ken Moseley in Columbia, S.C., Simon Golar in New York City, and Hosea Williams in Atlanta. Blacks already have lost one member of Congress, Rep. Katie Hall (D) of Gary, Ind., in the Democratic primary.
Within the next four years, blacks also may wield more power in the nation's big cities, Cavanagh says. Black mayors could be elected in New York City, St. Louis, Baltimore, and Memphis, he says. Blacks and Puerto Ricans could form a coalition to put Basil Patterson in the mayoral chair of New York, he adds. In New England, mayoral candidate Charles Tisdale, ''who came close in 1983,'' could be voted into office in Bridgeport, Conn., in 1985, Cavanagh says.
Black politicians see Jesse Jackson as a barometer for black political activity in the establishment of a nationwide black political network as well as in the presidential election. Democratic nominee Walter F. Mondale will speak at the Urban League convention. US Rep. Jack F. Kemp of New York will represent President Reagan.
''Jesse will set the mood for black voters in November,'' says Virginia's Benjamin Lambert (D) of the state House of Delegates. A member of the National Democratic Committee that is pledged to support the Mondale-Ferraro ticket, Mr. Lambert adds: Jackson ''has pinpointed black issues and causes to the American public. He has been placed in a tremendous leadership role no black has had in recent years. Many blacks are awaiting word from him before they commit themselves to how much backing they will offer the (Democratic) party.''
Jackson, in a July 25 speech, said he will concentrate on strengthening local political organizations and developing a national political network for blacks. He announced a campaign that includes trying to elect ''at least one black congressman in each state of the Deep South.''