A young Solidarity supporter tonight became the first officially confirmed fatality in the wave of strikes and demonstrations that followed the banning of the independent union movement by Poland's martial-law government.

The official Polish news agency PAP said 20-year-old Bogdan Wlosik was shot by a plainclothed policeman during rioting in the southern steel-making town of Nowa Huta yesterday and died on the operating table in a nearby hospital. PAP said the policeman had fired his pistol "to save his own life" after being chased by demonstrators.

The incident could conceivably add fuel to the disturbances, which had appeared to be on the verge of petering out today.

Friends of the dead man were reported to have built a memorial for him near the place where he was shot. Eyewitnesses said that, following an open-air service of commemoration, several dozen people were dispersed by police using tear gas when they tried to march on a local militia post.

Today's incidents in Nowa Huta, an industrial suburb of Krakow, were much less serious than yesterday's clashes, which went on until 2 this morning. According to official accounts, Solidarity supporters ripped up trolley tracks, burned newsstands and attacked public buildings after riot police attempted to break up a march by some 3,000 steelworkers.

Some of the demonstrators from the giant Lenin steelworks, the largest factory in Poland, were reported to have hurled stones and metal ball bearings at the police. PAP said 67 policemen were injured; 21 were said to be still hospitalized, including two in "a very serious" condition. The official account said 27 demonstrators had been injured and eight were in the hospital.

Officials said police detained 135 people in Nowa Huta and 174 in the southwestern city of Wroclaw, where there were also clashes last night.

The latest disturbances appear to have been impulsive and unorganized, and there is no evidence to support official claims that they were centrally planned. Underground Solidarity leaders have called on their supporters to take part in a nationwide four-hour strike Nov. 10, the second anniversary of the union's legal registration.

Nowa Huta, which was built as a model socialist community in the early 1950s, has been a flashpoint for unrest over the past few months. Steelworkers streaming out of the vast complex at the end of the first shift have repeatedly marched toward the town center on the 13th of every month -- in protest against the imposition of martial law on Dec. 13 -- and on several other occasions as well.

Secret police are routinely assigned to infiltrate crowds of demonstrators. Sometimes they have attempted to make arrests and at other times have been seen to incite crowds to acts of violence.

Ugly incidents have developed in several places when demonstrators have uncovered someone they believe to be working for the police--but today was the first time anyone had officially been reported killed as a result.

Last month police opened fire on demonstrators in Wroclaw and the nearby copper mining town of Lubin, killing four people. In the most serious violence since martial law was declared, at least 10 coal miners were killed when the Wujek mine near Katowice was stormed by police last Dec. 17.

Officials today for the first time acknowledged that there had been some unrest in the industrial region of Lower Silesia, which has been relatively peaceful since the early days of martial law. The official Interpress agency said that miners at the Jankowice mine near Rybnik had struck for a short time but later started work following "explanatory talks with management."

A worker at the Katowice steel mill was said to have committed suicide by throwing himself into a vat of molten steel while wearing a Solidarity badge on his lapel. Interpress said the cause of suicide was "serious . . . depression."

The official Communist Party newspaper Trybuna Ludu warned in an editorial today that this week's disturbances could, "contrary to the government's intentions, prolong the period of extraordinary measures." The military leader, Gen. Wojciech Jaruzelski, has set the end of the year as a target date for lifting martial law, provided social peace is maintained.