The first tentative steps were taken today to resolve a bitter impasse that has stalemated city government here for the last week.

Twenty-nine rebellious white aldermen sent a telegram to new Mayor Harold Washington agreeing to sit down for the first time with his supporters to negotiate the rules and organization of the City Council.

The group appointed six of its most seasoned members, led by Cook County Democratic Chairman Edward R. (Fast Eddie) Vrdolyak, to begin meeting with Washington supporters late tonight to resolve the battle over council control.

Vrdolyak's forces, who hold a 29-to-21 majority in the council, approved a controversial reorganization plan last Monday that gave black aldermen only three minor chairmanships of the council's 29 committees. The mayor's forces maintain that the reorganization plan was passed at an illegal meeting.

Washington, who walked out of two council meetings last week in protest, appealed Sunday to the rebel aldermen to negotiate "for the good of the city."

Washington considered today's response "a very positive and encouraging sign," said his press secretary, Grayson Mitchell. "We're closer to a settlement than we've been since this whole thing started . . . . "

Washington, inaugurated 10 days ago as Chicago's first black mayor, was at loggerheads with Vrdolyak's forces all last week. The battle climaxed Saturday in one of the most chaotic council meetings in city history, rife with name-calling, shouting and even the threat of a fist fight.

It was unclear today how much either side is willing to compromise, however. As a condition for negotiations, Vrdolyak forces demanded that Washington supporters present an organization plan of their own.

The mayor's supporters caucused for more than two hours this afternoon and agreed to a plan that would give eight committee chairmanships to blacks. Washington supporter Wilson Frost would be chairman of the powerful Finance Committee and Vrdolyak would head a minor committee overseeing plans for the 1990 World's Fair.

This apparently would set up another impasse: Vrdolyak forces want Edward Burke to head the Finance Committee and insist they will not compromise on the matter.

Roman Pucinski, a key Vrdolyak ally, said today that his side is firmly committed to keeping the 29 committees in place, but would be willing to negotiate on rules governing the body.

The next official council meeting is Wednesday. Washington has said he would like to have the dispute settled by then.