New York City transit workers reached a settlement this morning with the transit authority, shortly after backing away from a threatened strike--an action that would have stranded millions of subway and bus riders, crippled Christmas commerce and potentially endangered lives in this sprawling city of 7 million people.

Leaders of the 33,000-member Local 100 of the United Transport Workers union had implored their members not to strike after restraining orders were issued Tuesday. But a dissident union faction that had pushed most strongly for the labor action was still urging its supporters to stick to the strike plan late Tuesday as negotiations were continuing.

"I think it's going to be a normal day," Giuliani said before the settlement was reached. But he did not rule out the possibility of limited work actions today that could make the commute slow for some.

With the outcome of the tug-of-war uncertain early Tuesday night, city officials had moved forward with emergency transport plans for fleets of buses, taxis, ferries, shuttles and jitneys to be pressed into service to accommodate the 4.4 million daily bus and subway riders who would have been affected had a strike gone forward.

A strike would have left 4,000 buses idle and 656 miles of subway track silent--effectively hobbling a city whose dependence on public transport is heightened during the Christmas shopping and tourism seasons. Already gridlocked by heavy seasonal traffic, Manhattan's streets could have become virtual parking lots, though new emergency traffic patterns were designed to lessen the impact.

Playing the role he has so often of protecting a city under siege, Giuliani had taken a hard line against the union. He took the city's arguments to court, where state Supreme Court Justice Michael Pesce on Tuesday slapped a temporary restraining order on the threatened strike. Penalties for striking, according to the order, would be a $25,000 fine against each striking worker on the first day. The fine would double with each passing day. The same formula would apply to the union itself--a fine starting at $1 million, then doubling each day.

"I have no sympathy for anyone threatening to strike against the city of New York," Giuliani said.

But Tim Schermerhorn, leader of a dissident faction in the union, was quoted by the Associated Press as saying that such penalties "are part of a strike and people are willing to make sacrifices."

The union was demanding pay increases of 9 percent in each of three years. The Metropolitan Transit Authority had offered an increase of 9.25 percent over four years. Details of the final settlement were unavailable early this morning.

Giuliani said during a briefing earlier Tuesday that the strike threat was really about power within the union, with "out-of-control" dissidents "trying to exercise raw power" over union leadership.

He also warned that a strike would put lives at stake, especially the elderly and infirm, because emergency vehicles would have difficulty moving about the city as fast as they normally do. For that reason, one plan to lessen traffic congestion is to make several city streets off-limits to private vehicles. On the rest of the streets, an HOV rule would prohibit private vehicles carrying less than three people. These plans were on hold, the mayor said late Tuesday, because he did not anticipate a strike.

During New York's last transit strike, which went on for 11 days in April 1980, the city's streets and bridges were lined with armies of workers walking during what was relatively warm and sunny weather. This time New York faced the prospect of stranded "straphangers," as subway riders are known, facing long walks in freezing weather.

"I hope it doesn't happen, like everybody else, because I'm very dependent on the trains," said Nancy J. Rich, a singer and lyricist, who rides the subway into Manhattan from her Brooklyn home. "My husband and I would have to drive and there are just the two of us, we don't have a third party, and they won't let you come into the city without three people. So that would really hamper us and it would result in considerable loss of income."

In addition to the city's restraining order, the state had one--also ordered by Pesce on Tuesday. The state invoked the Taylor Law, a statute that prohibits public employees from striking. It calls for each worker to be docked two days' pay for every work day lost to strike action.

Those penalties are separate from the ones that can be levied by the city. In addition, the state also can impose fines on the union for contempt of court should the strike go forward.

The strike threat had been looming for weeks, and city emergency management officials scrambled to devise backup plans.

Jerome Hauer, director of the mayor's office of emergency management, said Tuesday that the city had acquired 700 extra buses, on loan from Illinois, Florida and elsewhere.

"We've pretty much tapped the market from as wide an area as possible," Hauer said, adding that "the buses are all coming in with drivers." And because of the strike, each bus was to have been equipped with two police officers for safety.

The city also was set to press its famed East and Hudson River ferry boat, the Circle Line, into transit duty. More ferry boats, 27 in all, had been borrowed from harbor cities such as Boston and Baltimore, capable of carrying up to 1,200 people each.

"The biggest concern we have right now is congestion" on the East River, Hauer said Tuesday.

Because of all the potential chaos, the city's 1.1 million schoolchildren had been told to stay home today in the event of a strike.

New York Transit At a Glance

Paid rides (average weekday): 5,146,677

Subway lines: 25

Bus routes: 227

Subway cars: 5,799

Buses: 3,867

Track miles: 656

Bus route miles: 1,671

Subway stations: 468

Employees: 42,881

SOURCE: Metropolitan Transportation Authority

CAPTION: Subway conductor checks to see if doors are clear at Grand Central Station on eve of a possible strike by subway and bus workers.