President Reagan yesterday dropped his policy of non-intervention in labor disputes and asked Congress to halt a potentially crippling nationwide rail walkout by imposing a settlement on 26,000 striking engineers.

Congress was expected to act quickly; hearings were scheduled in both House and Senate for today.

But there was some question whether Congress would force settlement terms on the union or simply order one more in a series of "cooling-off" periods.

The walkout by members of the Brotherhood of Locomotive Engineers began after midnight Saturday when a presidentially mandated no-strike period ended and contract talks stalled.

The engineers' action halted much of the nation's passenger and freight traffic, except in the northeast corridor.

Coal mines and auto plants began shutting down yesterday and commuters by the thousands were left looking for rides to work. Supervisors softened the early impact by keeping an estimated 50 or 60 percent of the more critical rail freight rolling. Freight trains carry almost all grain, as well as coal, steel and other such basic and heavy industrial materials.

Most railroads in the Northeast, including New York City, were spared.

Amtrak passenger trains were running "all normal service on the Washington-New York-Boston corridor," a spokesman said. The federally subsidized Conrail line was not a target of the strike and was running normally.

All passenger trains west of Chicago and south of Washington, and virtually all commuter trains in Chicago, San Francisco and Boston's north side reportedly were idled.

The negotiations snagged over the engineers' traditional status as the highest-paid rail crew members. They want the right to strike during the life of this contract if they lose that status; bargainers for the rail industry wanted them to give up the right to walk out on this issue.

The engineers historically have enjoyed a 15 to 20 percent wage advantage over their co-workers. But now they stand to lose it because management is paying some of their fellow rail employes -- such as conductors and brakemen -- extra in exchange for a reduction in the number of crew members.

The engineers union is the only one of 13 rail unions still without a contract to replace one that expired 18 months ago.

In announcing the president's decision at a White House briefing yesterday, Secretary of Transportation Drew Lewis said, "We think the issue is so narrow that it does not justify the damage it's going to inflict on the American public and the economy. . . . "

He acknowledged the administration is extremely reluctant to interfere in the collective bargaining process. But the president nevertheless agreed to seek a congressional resolution that would force the union to accept the recommendations of a special emergency board he named earlier in the dispute. If Congress goes along, the union would be forced to accept the no-strike provision, but would remain free to negotiate the wage issue.

John Sytsma, president of the engineers union, said yesterday his membership is "very law-abiding" and would honor any order from Congress.

If the strike continues, Lewis said, more than 450,000 people in rail-dependent industries would be out of work within a week. He estimated the loss to the economy initially at $80 million per day. (A spokesman for the railroad industry put the economic costs at "$1 billion a day and rising.") If the strike lasted two weeks, the layoff total would rise to 1 million, Lewis said. After 10 days, he predicted steel and auto plants would be shut down.

Lewis and Labor Secretary Raymond J. Donovan met with the president after consulting yesterday morning with congressional leaders. Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) had assured him the Senate would vote as soon as it could hold hearings.

Lewis spoke less confidently about what would happen in the House. He indicated that Chairman John D. Dingell (D-Mich.) of the governing Energy and Commerce Committee may not support the administration's precise resolution but has agreed to move it quickly to the floor.

Lewis indicated other transportation unions are not behind a continued strike because "the implications for them are just as serious as they are for the rest of the economy." Some of them are expected to testify today on Capitol Hill, he added.

Unions representing conductors, switchmen, clerks, mechanics and brakemen reportedly have agreed to honor the engineers' picket lines. The strike has idled some 300,000 rail workers.

Truckers were expected to pick up some of the freight, but, said an official of the Chessie System's Michigan-Ontario division, "Unless the engineers return to work at once, Michigan's automotive, steel and chemical plants soon won't be able to get enough raw materials by rail to keep producing."

General Motors officials announced the layoff of some 2,300 hourly workers at a St. Louis plant because it ran out of key assembly parts normally shipped in by rail.

Texas grain handlers reported the strike could delay getting this year's crop into storage and could hurt imports.

In the coalfields of West Virginia, Armco Steel officials announced the strike had forced them to lay off 1,400 workers at eight mines.