The battle between the government and its striking air traffic controllers was fought mostly in the courts yesterday, while the nation's airlines struggled for a second day to keep their passengers moving and their losses down.

The government mobilized more military controllers, bring to 370 the number who will act as backup to supervisory personnel and non-striking controllers, and President Reagan repeated his threat to fire any controller who is still on strike at 11 a.m. today.

"I have no choice," Reagan said. "The law is very explicit. they took an oath in writing that they would not strike. I think it's not a case of firing. I think they quit."

But if the administration has not changed its position, "neither are we changing ours," said Robert E. Poli, president of the striking Professional Air Traffic Controllers Organization (PATCO), indicting that the union intends to hold ranks even in the face of the president's threat and heavy court-imposed fines.

Concern about that strategy was voiced in Chicago yesterday by United Auto Workers President Douglas A. Fraser, newest member of the AFL-CIO's executive board. "This [the walkout] could do massive damage to the labor movement," he said, adding that Reagan could turn the strike into political gain.

The Justice Department was using its muscle to push striking controllers back to the towers, and was finding allies in federal courts around the country.

A federal judge in New York fined the union $100,000 an hour, twice what the airlines had sought, for as long as the illegal strike lasts. U.S. District Court Judge Thomas Platt found PATCO in contempt of his own 11-year-old injunction against strikes and slowdowns by the union.

Last night fines imposed Monday by U.S. District Court Judge Harold H. Greene went into effect. Starting at $250,000, the fines coud amount to $5 million by Sunday.

The Justice Department said it had obtained 40 temporary restraining orders, telling PATCO members that their strike is illegal and ordering them back to work, "in every federal area where there is a major airport," according to Justice Department spokesman Art Brill.

Meanwhile, the Federal Aviation Administration said the nation's air traffic was moving smoothly, if a little slowly. The airline dustry said it was losing a quarter of million passengers a day, some because the airlines could not accommodate them and some simply because they were staying away from air terminals.

But Transportation Secretary Drew Lewis and Federal Aviation Administration chief Lynn Helms said the companies were doing much better than expected under the circumstances. Helms said the nine major airlines were moving 83 percent of their scheduled flights, with delays late yesterday afternoon averaging 18 minutes. He said the longest delay recorded at that time was 91 minutes.

But the nation's 23 busiest airports, which carry 75 percent of the daily domestic commercial air travelers, were still under an FAA order curtailing their traffic by 50 percent. Helms said he hopes to be able to raise that ceiling to 75 percent today.

Lewis also said he hopes to have 50 to 80 percent of the striking controllers back on the job by the termination deadline today.

"If that's the case, we have no problem. If that's not the case, we do have a training school" in Oklahoma City, Lewis said, repeating his vow to carry out Reagan's dismissal order and to replace fired controllers with new employes.

Some striking controllers returned to their radar screens yesterday, but Poli said the number of returnees was small: 59 of the estimated 13,000 PATCO members who walked off their jobs at 7 a.m. Monday. The union has about 15,000 members, which would make the strike about 84 percent effective, according to PATCO calculations.

PATCO also got some moral support yesterday from the American Civil Liberties Union.

Calling the administration's termination threat an unfair labor practice. ACLU executive director Ira Glaser said Reagan was "acting like any other union-busting employer" in threatening to fire all striking controllers.

Federal authorities cite several portions of the U.S. Criminal Code that provide for penalties against federal workers who violate their oaths not to strike against the government. the penalties include dismissal, barring from future federal employment, fines up to $1,000 and jail terms up to one year.

However, Lewis acknowledged yesterday that the mass dismissals could turn into something of an administrative ordeal. Under normal circumstances, for example, the government must give its employes 30-day dismissal notice.

But he implied yesterday that the administration will move under the portion of the 1978 Civil Service Reform Act that says 30 days' advance notice should be given "unless there is reasonable cause to believe the employe has committed a crime for which a sentence of imprisonment may be imposed."

Under those terms, Lewis said, any controller dismissals might become effective within seven days after notice is given, because participation in a strike against the federal government is a prosecutable offense, punishable by imprisonment.

"Whatever it takes to get the terminations, we're prepared to do it," Lewis said.

Short of the firings, some union leaders and their locals already have been found in contempt of court, and fines have been levied against them. Judge Greene in Washington found Poli in contempt Monday night and fined him $1,000 a day, but Greene rejected a Justice Department request to jail Poli.

However, U.S. District Court Judge Oren R. Lewis in Alexandria indicated that he would have no compunction against jailing leaders of locals from National, Dulles and the Leesburg control center. Lewis found the three locals and their leaders in contempt of court yesterday and said he would jail the leaders "unhesitatingly" if they did not comply within a five-day period of a restraining order signed yesterday.

The locals also were fined $50,000 a day, and the leaders $1,000 a day, for the five-day period. Lewis ended the hearing by telling the three controllers that, if they do not return to work within that time, "I will consider a motion by the government to put you in jail and i probably will do it."

Meanwhile, the government is refusing to negotiate with the union while the strike is in progress.