NEW BEDFORD, Mass. (AP) _ The mayor of this strike-torn port said Tuesday that two fires, tire- slashings and alternative auctions by non-union boats have undermined chances for a speedy, peaceful settlement to the 34-day-old fishermen's walkout.

''It's especially frustrating to have the violence occur because every time it does, it seems to set us back a week or two,'' said Mayor John Bullard of the strike which began Dec. 27.

''I don't know how long (a resolution to the strike) would take under the best of circumstances,'' he added. ''But now the case is complicated by extraneous situations like the fish exchange, fires and tire-slashings.''

On Tuesday, Bullard asked City Solicitor Rosalyn Brooker to seek a court injunction to stop dealers and independent boat owners not involved in the strike from participating in an alternative auction at the New Bedford Seafood Exchange Inc. It could be a week before Bristol Superior Court rules on the matter.

Bullard said he was opposed to the alternative auction because it violates a New Bedford ordinance banning boats from unloading fish that won't be sold at a city auction.

Four draggers sold fish at the latest alternative auction Tuesday morning, and one or two buyers were given $50 fines, said Police Officer Raymond Furtado. About 25 fishermen, marching three at a time, peacefully picketed the auction, Furtado added.

A man who answered the phone at the 600-member Seafarers International Union in New Bedford said Tuesday that the striking fishermen had no comment. There was no answer at the boat owners' headquarters.

The two sides broke off negotiations last week and none were planned Tuesday. The dispute centers on the division of proceeds from the sale of fish.

''They haven't even set a date,'' said Bullard. ''I think the mediator wants everyone to cool down a bit.''

Meanwhile on Tuesday, fire officials continued to investigate two fires that they have labeled ''suspicious.''

The first ignited Monday night at a marine electronics shop and a boat supplier and caused $250,000 damage.

A second fire, erupting at New Bedford Marine Electronics, caused $40,000 damage to equipment, according to Ron Pontes, company president.

Tires were slashed Monday on a vehicle parked outside the auction house.