DEARBORN, MICH., SEPT. 14 -- United Auto Workers union leaders and Ford Motor Co. officials tonight agreed to extend their current labor contract on a day-to-day basis, averting for the moment a nationwide strike against America's second largest auto maker.

The reasons for the extension are twofold. Representatives of both sides said they needed the extra time to come up with a solution to cost and implementation problems raised by the union's tough demands for job security. Also, the negotiators said they simply needed time to rest after nearly 40 hours of bargaining over the weekend.

"I am very tired and the whole staff is very tired," UAW President Owen Bieber said of his union's efforts. However, for the first time in two weeks, Bieber said that the union and company have "made substantial progress on the central issue," which involves the union's proposal for a three-year, no-layoff contract.

Ford bargainers, too, agreed that progress has been made on the controversial issue. But, "It's going to take a while longer for us to overcome the problems" inherent in the potentially costly proposal, said Stanley J. Surma, Ford's chief negotiator.

Sources close to the negotiations said tonight that the two sides actually are quite close to an agreement on the no-layoff proposal. However, the sources said that the dollars and cents issues still need to be worked out and that the union and the company were still trying to find a way to handle sensitive issues, such as combining jobs in skilled trades categories. Apparently, according to sources, union leaders representing skilled trades groups such as tool and die workers fear that their members will be forced to do jobs outside of their current job classifications.

{Meanwhile, in Toronto, Chrysler Corp.'s 10,000 Canadian workers launched a strike early Tuesday after weeks of negotiations with the auto maker failed to produce a settlement.

Workers at four Ontario plants walked out at midnight when their contracts with Chrysler Canada Ltd. expired, said Canadian Auto Workers spokesman Wendy Cuthbertson.

Chrysler's Canadian plants produce all of the company's full-size vans and most of its hot-selling minivans. They also produce numerous components used in the United States, and a strike of more than a few days' duration would force Chrysler to begin closing U.S. operations as well.}

Bieber asked the UAW's 53 locals at 85 Ford facilities in the United States to have patience and to stay on the job until further notice, a request that won praise from Peter Pestillo, Ford's vice president for employe and external affairs.

"It takes courage" for a union leader to ask his people to stay on the job past the technical expiration of a contract deadline, Pestillo said. The usual practice, particularly in the UAW, is to adhere to the doctrine of "no contract, no work," Pestillo said.

Bargaining is expected to resume early Tuesday. Pestillo held out the possibility that an agreement might be reached sometime Tuesday, during the day, an unusual occurrence in an industry where settlements often come in the wee hours of the morning.

Neither Ford nor UAW officials would offer any details of progress on the job security issue.

However, sources close to the negotiations say that the company has agreed on the concept, and that what remains to be done is to work out the economics and practical implementation of the job security package.

Once those details are taken care of, no small feat, wages, benefits and other matters can be handled, sources said.

Earlier today, the UAW locals representing workers at 85 Ford facilities around the country were preparing their members for a walkout.

At Norfolk, where Ford assembles pickup trucks, UAW Local 919 President Tom Cusick spent the day at the plant, talking to members and going over picket-line schedules and procedures.

Ford's Norfolk assembly plant employs 1,640 assembly workers.

Ford has been struck three times before -- in 1961, 1967 and 1976 -- in its 46-year relationship with the UAW.

The longest walkout, in 1967, lasted 66 days.

The UAW chose Ford as its strike target in the current negotiations with Ford and General Motors Corp., because Ford is on a roll. In a historic turnabout, Ford has become more profitable than its much larger rival, earning $3 billion in the first half of 1987, compared with $1.9 billion for GM.

Ford has a cash and securities reserve totaling $9 billion, the legacy of aggressive cost-cutting in the late 1970s and early 1980s and the reward for turning out consecutive hits such as the Taurus and Sable midsize cars and a best-selling line of pickup trucks.

Ironically, according to some sources, the UAW also chose Ford as a target because the union believed it would have an easier time of it at the No. 2 auto maker. Over the years, Ford has built up a reputation for having better labor-management relations than GM.

At the outset of the talks many auto industry analysts thought that GM would be the most likely to actually suffer a strike -- largely because GM is doing what Ford already has done, closing down assembly and component plants deemed noncompetitive.