Union spokesmen for about 36,000 copper workers striking nationwide say they'll reconvene Saturday evening in Phoenix to consider a new offer by Kennecott Copper Corp., the nation's largest producers.

A settlement with Kennecott might prompt other companies to follow suit, the union spokesman said, but representatives of copper firms say Kennecott's offer is far above what they can afford.

Copper workers whose three-year contracts with seven companies ended at midnight Thursday immediately set up picket lines against the producers - the Anaconda Company. ASARCO Inc., the Cities Service Company, Inspiration Consolidated Copper Company, Phelps Dodge Corp., U.S. Metal and Kennecott. Contracts with an eighth producer, Magma Copper Company, were to expire at midnight today, with negotiations expected to continue up to the deadline.

Kennecott, whose earlier offers had come closest of all the firms to the unions' demands, made another proposal at mid day to leaders of more than two dozen striking unions. Cass Alvin, a spokesman for United Steelworkers of America, said the company's newest offer apparently included straight time wage increases of about 85 cents an hour.

Union representatives led by the steelworkers, who represent the largest number of employees in the copper coalition, have asked for straight time pay increases totaling about 94 cents an hour over the next three years. They also asked for additional fringe benefits, continued cost of living provisions like those now in contracts and the settlement of various local issues.

Alvin said the National Nonferrous Conference, a policy-setting group of union representatives that adopted the strike resolution Thursday, would meet again at 6 p.m. Saturday to consider Kennecott's offer. "I think by that time wil be in the form of a tentative agreement" that could be the lead settlement to end the strike, he said.

But H. Myles Jacob, Inspiration chairman, said he was "appalled by the offers" made by Kennecott and others. His company has offered a 43-cent-an-hour wage increase.

"It appalls me too - and me to the list," said M. P. Scanlon, spokesman for Phelps Dodge, the largest copper employer in Arizona. "But we've got to be realists."

Scanlon said, however, that his company would not decide what steps to take next until details of the Kennecott offer are known and whether the union would accept it.