Hopes for an end to the strike that has halted most iron ore production in the country for 16 weeks rose yesterday as 800 Michigan miners voted to return to work and union officials predicted another 3,700 workers would end their walkout shortly.

The strike - the longest major work stoppage of the year - has idled 15,000 members of the United Steelworkers, who mine and process two-thirds of the nation's iron in Minnesota and Upper Michigan.

A major breakthrough in the strike came during the last two weeks as industry negotiators agreed to bargain over union demands for incentive bonuses for high production and to permit settlements on a local basis. Industry officials previously insisted that incentive pay was a national contract issue covered by the industry-wide no-strike agreement.

The USW strike has been based on a contention that incentive pay is a local issue not covered by the no-strike agreement.

An industry offer now under consideration by union workers would give most ore workers roughly the same incentive bonuses that steel mill workers now receive, after November, 1979. Unlike a previous industry offer, workers who are not eligible for incentive pay would be protected against any wage losses.

This would nearly make up the 65-cents-an-hour wage differential between steel workers and iron miners, who now earn an average of about $7.40 an hour, according to union officials.

The first back-to-work vote since the strike began Aug. 1 came Sunday night at the Cleveland Cliff Iron Co.'s Tilden Mine in Negaunee, Mich., according to the Associated Press.

Votes were scheduled last night at three other Cleveland Cliffs mines in Upper Michigan. Union officials predicted ratification of the contract offer.

Gary Hubbard, a USW spokesman, was quoted by the AP as saying the Michigan settlement would "encourage more intensive bargaining on the Minnesota [iron] range," where most of the strikers work.

Existing iron ore supplies, augmented in some cases by imports, were sufficient to sustain steel production, but the strike was reportedly beginning to hurt soe independent ore companies.

There had been concern that the strike could jeopardize continuation of the no-strike agreement over national issues after the current contract's expiration in 1980 if the industry felt threatened with local strikes over issues it considered to be national in scope. As a result, the companies won agreement from the iron ore workers that disputes over whether issues are local or national henceforth will be submitted to arbitration, without a strike.