GAZA CITY, DEC. 23 -- Israeli security forces, helped by a steady downpour, reimposed order in the occupied Gaza Strip and West Bank today, rounding up hundreds of alleged rioters, sealing off two refugee camps and showing an increased military presence throughout the territories wracked by two weeks of violence.

The Army gave no figures for the number of arrests, many of which took place during the night, but large tents were raised inside the barbed-wire perimeters of the Ansar Two military prison here and the Fara prison in the West Bank. A military spokesman said that "all the prisons are full all over Israel."

The Palestine Press Service said more than 350 arrests had been made and put the total number of detainees at 1,770, The Associated Press reported.

"We are arresting the inciters and the stone-throwers," added the spokesman, who insisted on anonymity. "They thought before that we were weak because we talked about being tough but we did not act. Now they can see we mean what we say."

Military authorities said the Army crackdown was a shift in tactics away from direct confrontations with stone-throwing mobs to mass arrests and other security measures. The idea was to halt the violence without increasing the death toll, which officials place at 21 and which they see as a major factor in the strong international criticism of Israel's handling of the disturbances.

Meanwhile, the government rejected the Reagan administration's strong statement condemning Israel's "harsh security measures" as well as the violent Palestinian demonstrations and Washington's refusal to veto a U.N. Security Council resolution deploring Israeli policies.

The Israeli statement, which a senior official here described as "middle of the road -- we feel more sorrow than anger at the United States," warned that the American position might give support to "extremist elements who encourage violence" and might harm Israel's efforts to restore order to the area.

{The Reagan administration publicly appealed to Israel again Wednesday to end its use of lethal force in the occupied territories. Details, Page A10.}

Palestinian leaders in Gaza, including former mayor Rashad Shawa, said the prisons were so full that many of those rounded up were being held for several hours, beaten by soldiers or security agents and then released.

Israeli television quoted an unidentified prisons official as saying that dozens of convicted criminals had been freed today to make room for the new security prisoners.

At Shifa Hospital here, scene of large-scale rioting several days ago, doctors said they were treating 30 or more Palestinians daily for broken limbs, cuts and bruises inflicted by soldiers.

"They caught me, handcuffed me from behind and hit me with clubs," said a young patient named Mohammed, whose right hand was in a cast and who displayed two stitches on his head and cuts on his face, back and legs. "Then someone hit me with a garbage pail lid, and they threw me against the wall like a pair of shoes."

A military official said such incidents "certainly could happen. They are not supposed to, but you must remember that the situation in Gaza has been very nasty. Maybe it's better to have a broken arm or to be in jail than to be shot."

Under military regulations, the Army can detain suspects for up to six months without charge or trial.

Defense Minister Yitzhak Rabin told a raucous session today of the Knesset, Israel's parliament, that military commanders would continue to order detentions at whatever rate they considered necessary to quell the disturbances.

He also said he would approve the deportation of alleged ringleaders regardless of whether such measures worsened Israel's image abroad.

Despite shouts of disapproval from left-wing legislators, Rabin defended the Army's controversial use of marksmen and high-powered sniping rifles to shoot rioters.

"They can shoot to hit leaders of disorder, throwers of firebombs, as much as possible at the legs after firing in the air fails to disperse the riot," he said. "As defense minister, I am responsible for the lives and safety of the soldiers and border police, and it is my duty to give them the means to defend themselves."

Most of the shops in this area remained closed as youth leaders continued to impose a 10-day-old commercial strike.

Many streets were filled with rubble and debris from burning tires and other makeshift barricades thrown up by demonstrators last week.

But thousands of Gazans traveled to Israel early this morning to go to work for the first time in more than a week, a move that leaders said signaled both their exhaustion with two weeks of nonstop violence and their need to earn money.

Many West Bankers also returned to their jobs, joining thousands of Israeli Arabs who went to work yesterday after staging a one-day general strike on Monday in sympathy with Arabs in the occupied territories. Steady rainfall throughout today and the Army's decision to keep about 900 elementary schools closed until early January also contributed to the lull, according to residents and military officials.

"I think things have calmed down and within a day or two they should return to normal in appearance," said Gaza leader Shawa, who is considered a moderate, in an interview. "But people are boiling inside. They are tired, they are frustrated and they are still very, very angry. Things can start up again very quickly."

The Army appeared to maintain a lower profile in the area, with troops massed outside the main refugee camps and towns but few patrols visible inside populated areas. Those who were seen moved in groups of 20 or so, unlike the small foot patrols that had attracted rioters in the first days of the violence.

An exception to the air of near normality was the Jabaliya camp, Gaza's largest, whose entrances were sealed off by barbed wire coils and whose estimated 10,000 workers were not allowed out to go to jobs. A curfew was still in effect following last night's violence in which a 17-year-old boy was shot dead by soldiers and at least three others were wounded.

In an account similar to those it has given after virtually every shooting incident, the Army said that a patrol had been surrounded by rock-throwing youths and had fired only when soldiers' lives were endangered. But witnesses, including a wounded youth at Shifa Hospital and an employe of the U.N. Relief and Works Agency, which operates the refugee camps, said the soldiers were not surrounded and could have backed away from the confrontation.

Bernard Mills, director of UNRWA operations here, said in an interview that he had been at the scene shortly before the shooting and that about 25 soldiers had advanced across an empty field toward stone-throwing youths. When he left, Mills said, the youths and the soldiers were about 200 yards apart and none of the stones had fallen near the troops.

Within 10 minutes of his departure, he said, cars overtook his vehicle with casualties from the shooting. "There was no danger to the Army," said Mills. "One can only conclude that this was a punitive action. They had all the reinforcements they needed. They've used this claim of patrols being trapped many times recently, and in many cases it's very doubtful."

Mills said the Army's actions at Jabaliya contrasted with its approach at other refugee centers in recent days. Large demonstrations have been allowed in the town of Rafah and at the Bureij camp, and no confrontations resulted.

"It was a smart approach," he said. "There was a lot of noise, and the steam went out. But Jabaliya is our largest camp, and there is a big police station and Army post right in the middle. I'm very sorry to say this, but it is a Sharpeville in the making" -- a reference to the South African township where 69 blacks were shot dead by police in March 1960.

At the Dehaishe refugee camp outside Bethlehem on the West Bank, soldiers erected barricades of barbed wire and cement-filled oil drums, preventing cars and trucks from entering or leaving by the main entrance. Only pedestrians were allowed through.

A military official said the action was taken following Monday's disturbances when residents blocked the Jerusalem-Hebron highway outside the camp. The official said residents could still enter and leave by smaller side roads at the back of the camp.

The Israeli government statement, issued by Foreign Ministry spokesman Ehud Gol, said there was "no foundation or justification for blaming Israel about the recent serious and unfortunate events" in the occupied territories.