By STEVEN GREENHOUSE

In demonstrations and marches in 70 cities, the labor movement seized on International Human Rights Day yesterday to begin a campaign asserting that American corporations routinely violate an internationally guaranteed right: the right to unionize.

Organized labor has begun this campaign to help persuade Congress to enact a law making it easier to unionize and to draw attention to thousands of instances each year in which they say companies break the law to beat back unionization drives. The bill would increase penalties on employers who fire workers for supporting unions and would allow workers to choose a union by signing cards instead of holding an election.

Pointing to polls showing that 42 million Americans would join a union if they could, union leaders said corporate America's resistance to unionization was the main reason union membership had fallen. The percentage of American workers in unions is 13 percent, down from 35 percent in the 1950's.

On Wall Street, John J. Sweeney, the A.F.L.-C.I.O.'s president, said, "There are more than 40 million workers in our country who say they would join a union in an instant if they could — but they are prevented from doing that by employers and antiworker elected leaders who have systematically stolen the freedom to organize from workers."

Reflecting some success in building popular support for their campaign, unions persuaded Atlanta's mayor, the executive director of Amnesty International U.S.A. and two Democratic presidential candidates, Howard Dean and Dennis J. Kucinich, to attend labor rallies yesterday.

Many corporate executives and labor critics assert that union membership has fallen because many unions are out of touch with workers' needs and because workers see no need for a union. "The reason they can't reverse their decline in membership is they can't come up with an agenda relevant to today's work force," said Randel K. Johnson, vice president for labor, immigration and employee benefits at the United States Chamber of Commerce. "They keep using rhetoric out of the 1930's that employers are bad and that the labor laws are weak. The labor laws haven't changed since the 1950's when union membership was at its height."

In rallies in Atlanta, Washington and Cleveland, labor leaders said a Cornell University study had found that corporations fired the most outspoken union supporters in one out of four organizing drives. Union leaders also complained that it often takes years for the National Labor Relations Board to reinstate fired workers and by that time unionization drives have often fizzled.

In New Haven, 103 workers and students were arrested for blocking the streets in a protest calling for labor rights.

"There is little enforcement and what enforcement exists is ineffective," James P. Hoffa, the Teamsters president, said at a rally in Atlanta.

Yesterday's labor gatherings resembled political rallies as some Democrats embraced labor's cause in part to shore up their labor support. At a meeting with union activists in Concord, N.H., Dr. Dean said this was "the right to have not only globalization of multinational corporations rights, it's also about the right to globalize workers' rights."

At a rally by several hundred union members in front of the Labor Department in Washington, Senator Edward M. Kennedy, Democrat of Massachusetts, said, "We want this administration to stop being the most antiworker, antilabor administration that we have seen."

Then, Gerald McEntee, president of the American Federation of State, County and Municipal Employees, called President Bush "the most antiworker" president and said the Bush administration had "launched unprecedented assaults against working families" by trying to end overtime pay for eight million workers and by "trying to bust federal unions like never before."

Responding to Mr. McEntee, Ed Frank, a Labor Department spokesman, said, "What else would you expect from the head of the A.F.L.-C.I.O.'s partisan political committee? The reality is that we have positive working relationships with numerous labor unions."