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Jesse Jackson made a dramatic attempt Friday night to mediate a dispute over who should succeed the late Mayor Harold Washington but failed to resolve a rift that threatened to rupture the black solidarity that put Washington into office.

The lack of agreement prompted renewed talk that black leaders who have focused on three aldermen-Eugene Sawyer (6th), Timothy Evans (4th) and Danny Davis (29th)-may have to turn to a new, compromise candidate.

After a series of meetings that began as soon as Jackson stepped off a flight at O`Hare International Airport and continued until shortly after 11 p.m. at a Loop office, black and Hispanic leaders called it a night with no agreement over who should be supported in a campaign for acting mayor.

”Whatever was being deliberated or prayed over in secret did not translate into a name, it translated into a process,” Jackson said after a two-hour session at his campaign office, 30 W. Washington St.

Despite rumors that an agreement was near that would anoint Evans for the mayor`s post, allies of Sawyer emerged with resolve that they will keep pushing his campaign.

”I just see that Sawyer will be the guy,” said Ald. William Henry

(24th), who orchestrated Sawyer`s campaign.

”Unity, that`s what we`re working for,” Sawyer said as he quickly left the meeting.

City Treasurer Cecil Partee, asked if an agreement had been reached, said simply, ”I don`t think so.”

Interim Mayor David Orr on Friday said that he would block any attempt to hand the post of acting mayor to someone from outside the City Council.

Some have suggested that an alderman could resign so a high-profile politician could be appointed to that seat, then be selected acting mayor.

”I will not go in for that chicanery,” said Orr, who would have to submit a name to the council for such a scheme to work. ”I would not appoint anyone from whatever side for that purpose.”

Jackson`s arrival at O`Hare International Airport was reminiscent of politicians jockeying for position near a mayor at a St. Patrick`s Day parade, Evans and Sawyer stood shoulder to shoulder with Jackson while numerous other politicians pressed in behind him and television cameras recorded his arrival. The two aldermen waited anxiously for Jackson`s commercial flight from Frankfurt, West Germany, to arrive, aware that their respective bids could hinge on how they are viewed by the nation`s most visible black figure.

Although Jackson has spoken favorably of Evans and is believed to be pushing for Evans` selection by the council, he made no endorsement.

”Whatever decision we make will be a collective one,” Jackson said at an airport press conference. ”We want to keep the team together. Hopefully, by tomorrow morning, there will be a more fitting decision as to what the recommendation of the alderpeople will be.”

But Evans` closeness to the mayor, his support from many of those identified with the reform movement and his popularity at Operation PUSH, Jackson`s widely known community organization, appears to give him an edge for Jackson`s support.

The council by law can elect an acting mayor who would serve until a special mayoral election, which is likely to be held in 1989. Interim Mayor David Orr will retain that post until an acting mayor is chosen. That decision could be made as early as Tuesday. The victor will need the votes of at least 26 of the 50 aldermen.

Jackson said he is not interested in running for mayor.

At the airport, nearly 20 politicians-congressmen, state legislators and council members-crowded around the exit from the customs area of the terminal as they waited for Jackson`s arrival. Airport security guards and Secret Service agents newly assigned to protect the Democratic presidential candidate had trouble keeping the group from flooding the arrival area.

The jockeying for position continued in the motorcade. State Rep. Carol Moseley Braun (D., Chicago) forced her car into the tail end after police tried to block her way, then relented.

Despite the homage to Jackson, several black leaders who support challengers to Evans said Jackson should not try to anoint a candidate for mayor.

”He should pray for us and he should give us advice and counsel, but he shouldn`t tell us who should be the mayor,” Ald. Henry said. ”That should be left up to us.”

Freshman Ald. Keith Caldwell (8th), who has also lined up with Sawyer, said he would listen to Jackson`s advice but didn`t expect to change his mind. ”Rev. Jackson is an extremely important individual, but in this matter, he is a citizen of Chicago, and his voice should be listened to just as I would listen to my ward,” Caldwell said. ”Gene Sawyer embodies those qualities that can bring our city together.”

Sawyer is believed to have support from 10 aldermen, including himself. They are Henry, Caldwell, William Beavers (7th), Lemuel Austin (34th), Robert Shaw (9th), Jesse Evans (21st), Allan Streeter (17th), Ernest Jones (20th) and Sheneather Butler (27th).

Evans is believed to have strong support from nine aldermen, including himself. They are Orr (49th), Dorothy Tillman (3d), Helen Shiller (46th), Bobby Rush (2d), Luis Gutierrez (26th), Raymond Figueroa (31st), Jesus Garcia (22d) and Juan Soliz (25th).

Sawyer`s aides believe they may be able to win over Soliz, despite the four Hispanic aldermen`s vow that they will vote as a bloc.

Ald. Lawrence Bloom (5th), expected to be in Evans` camp, suggested that he may become a candidate for acting mayor.

Evans also picked up support from influential black independent leader Lu Palmer, who said Friday that an informal poll found that callers to his weekly radio program ”overwhelmingly” supported Evans.

Sawyer allies meanwhile bristled at suggestions that he would represent a return to Democratic machine politics.

”The old administration is trying to make us look like the old guard,”

Henry said. ”But Gene Sawyer was the first to support Harold Washington, he started the movement, not anybody else.”

Sawyer was the first alderman to endorse Washington and delivered whopping vote totals from the 6th Ward for the mayor.

He said he has made no efforts to drum up commitments from other aldermen but is expected to get support from Aldermen Ed Smith (28th) and Percy Giles

(37th). Aldermen Marlene Carter (15th) and Anna Langford (16th) remain uncommitted.

That leaves 25 aldermen from lakefront and white ethnic wards as the balance of power in the race to succeed Washington. They have hardly given up on fashioning a coalition that could elect a white mayor.

Aldermen from the white ethnic wards are expected to caucus on Saturday in an attempt to reach a consensus on a candidate. Names being considered include Ed Burke (14th), Richard Mell (33d), Michael Sheahan (19th), William J.P. Banks (36th) and Terry Gabinski (32d).

Although Jackson had conferred with black leaders by telephone en route from an aborted trip in the Middle East, he also has been in touch with such white leaders as Ald. Roman Pucinski (41st) and his daughter, Aurelia, the Democratic-slated candidate for clerk of the Cook County Circuit Court.

Jackson indicated that he will support the entire county Democratic slate, which could help Pucinski in the black community and pull some whites toward a coalition with a Jackson-backed candidate for mayor.

If Sawyer can hold 10 black votes in line through the weekend against pressure from Jackson to join Evans, he could be in position to claim the mayor`s chair.

Sawyer forces believe the white ethnics won`t reach a consensus and couldn`t fashion a 26-vote majority if they did. Therefore, many of them, Sawyer`s thinking goes, will respond to the strong overtures from his camp.

Those overtures are likely to include a promise to scale back the $2.7 billion budget and $84 million property-tax revenue increase proposed by Washington.