The future of the steel industry's no-strike agreement and union demands for increased job security were at stake late yesterday as labor-management negotiators struggled against a self-imposed deadline to settle a new three-year contract.

Local union officials began arriving at the Shoreham Americans Hotel for a contract ratification meeting today but there was no word on the progress of the negotiators, who were described early yesterday as being cautiously optimistic that a settlement could be reached without arbitration.

The existing contract covering 340,000 union workers in the 10 largest steel companies prohibits a nationwide strike, providing instead for outside arbitrators to resolve disputes.

Although the contract does not expire until July 31, last night was the mutually agreed on target for concluding negotiations. Unresolved issues are to be presented to a jointly chosen five-member arbitration panel April 20, leaving some leeway for extension of the deadline.

Both sides have been described as anxious to avoid arbitration because of mutual distaste for resolution of their disputes by outsiders and because failure to negotiate an agreement could signal an end to the experimental no-strike clause, first used in the industry's 1974 barganing.

Lloyd McBride, president-elect of the United Steelworkers, said during his campaign for presidency of the union earlier this year that the strike ban would probably be dropped for the future if this year's contract had to to to arbitration.

One of the windfalls of the existing no-strike agreement is a guaranteed 3 per cent a year increase in worker's wages, now averaging slightly more than $8 an hour, plus automatic cost of living raises, over the life of the new contract.

With guaranteed wage increases and cost-of-living adjustments already in hand, the union has focused on what it calls "lifetime security" for steel workers - a goal that other unions such as the communications workers are also pursuing this year as a protection against economic uncertainty.

Among proposals reportedly being discussed as the union scaled down its initial position under industry pressure were extension to 40 hours of the guaranteed 32 hours' pay for any week during which a worker put in any time on the job.

The union reportedly was also pushing for restrictions on contracting of work to outside firms when its own members are availble for jobs. Without some industrywide protections against contracting out work, the union wants the issue left to local plantlevel bargaining, which is not subject to the no-strike provision and thus could lead to walkouts later this year.