Thousands of people demonstrated their support for the besieged Polish Solidarity labor movement at 16 rallies in the United States as well as at demonstrations in Vienna, Tokyo, London, Brussels, and several cities in West Germany during "Solidarity Day" gatherings yesterday.

In Washington, an array of political leaders was among the hundreds who attended a Mass before a march to Lafayette Square across from the White House.

The largest of the rallies was in Chicago, the city with the largest ethnic Polish population outside Warsaw, where Secretary of State Alexander M. Haig Jr. sang a Polish song and declared to the cheers of about 8,000 that America "will not do business as usual with Poland or the Soviet Union while repression continues in Poland."

Haig said the "sight of a peaceful people seeking peaceful change has terrified" the government of Gen. Wojciech Jaruzelski and the Kremlin.

"But the action of those fearful men will not deprive the Poles of their faith, their courage or their sacred dreams," he said. "Change will come. Hope will be reborn, and Poland will be truly Poland again."

Then Haig said in Polish: "Jeszcze Polska Nie Zgniela" (Poland has not yet perished) and sang out the chorus of a traditional Polish song, "Sto Lat" (May you live 100 years).

The crowd chanted the words again and again, then enthusiastically applauded Haig.

Those at the rally carried "Solidarnosc" banners, posters of Solidarity leader Lech Walesa and protest signs. According to wire reports, one sign read, "Send Russia Our Wheat in a Nuclear Missile."

Many western political leaders added their videotaped voices to the echoes of the rallies as they participated in an International Communication Agency-produced television show "Let Poland Be Poland," offered for broadcast today to some 50 broadcast services around the world.

Among the leaders who will appear are President Francois Mitterrand of France, Chancellor Helmut Schmidt of West Germany, and the prime ministers of Norway, Great Britain, Belgium, Portugal, Italy, Luxembourg, Iceland, Australia, Spain, Japan, Turkey and Canada.

The Soviet news agency Tass blasted the program, saying, "The White House has . . . decided to stage in Washington cheap shows in Hollywood's 'best tradition,' that is, boisterous and vociferous spectaculars with as little meaning as possible."

The AFL-CIO organized gatherings in all 50 states yesterday to mark American labor's solidarity with the Polish movement.

In Washington, Roman Catholic Archbishop James A. Hickey celebrated a special Mass at noon before some 800 people inside St. Matthews Cathedral. Hickey denounced "the prolonged miseries of martial law" in Poland and asked Washingtonians to pray for Poles "deprived of their basic human right to participate freely in the destiny of their country."

In the audience was Zbigniew Brzezinski, national security adviser to President Carter, as well as dozens of area labor leaders and leaders of local Polish and other ethnic groups.

More than 1,000 people marched quietly down 17th Street to Lafayette Park in front of the White House, where two men draped a Solidarity banner around the statue of 18th-century Polish Gen. Thaddeus Kosciusko.

Many of the marchers wore Solidarity pins and armbands. Polish emigres and Americans of Polish descent were accompanied by Hungarians, Czechoslovakians, Latvians, Estonians, Afghans and Vietnamese. Most of the marchers were older persons, well-appointed suburbanites. Younger couples brought their children.

"We're very sad about the whole thing," said Chester Kowalczyk, a retired Navy Department cartographer from Silver Spring. "The Russians cannot take this," he said, waving a Polish flag. "The more opposition we show, the better chance we have."

"I think it's marvelous," said Joanna Trzcinka of Alexandria as she watched the rally. "I have five kids and they're all proud of their roots. Very proud of their roots."

The marchers later packed the lobby of AFL-CIO headquarters less than a block away, where Sen. Henry M. Jackson (D-Wash.) drew cheers and enthusastic applause. Solidarity efforts to win freedoms from the communist government "will be remembered long after their puppet government has passed from the scene . . . . The military regime is in deep trouble," Jackson said. "No solution to Poland's problems is possible without the participation of Solidarity."

About 300 people gathered at a rally in Boston to hear speeches from Massachusetts Gov. Edward King, Sen. Edward M. Kennedy, and Cardinal Humberto Medeiros. Kennedy told the crowd, "What we are seeing in Poland is repression by proxy. It is the dark work of a regime and an army acting under the shadow of Soviet bayonets . . . . The military rulers of Poland have lost the right to call themselves Polish."