People pushing baby strollers, holding toddlers and carrying union signs gathered Saturday near the Washington Monument in support of so-called "family" legislation for working parents and the elderly.

"Hurrah, hurrah for the American family," said Rep. Claude Pepper, D-Fla., 87, the oldest member of Congress and a champion of bills to expand job and medical benefits for working parents and senior citizens.The rally was sponsored by a coalition of labor organizations, and religious, civil rights and women's groups. About 3,000 people were in attendance, according to Officer Maria Gonzalez of the U.S. Park Police.

"Let us rededicate ourselves to the sanctity, to the nobility and the well-being of the American family, the base of our great society, the base and strength of our great America," said Pepper, as rally participants cheered.

The event at Washington's big outdoor pedestrian mall featured entertainment for the children, such as a Chinese lion dance and trampolines. Adults marched with union signs or set up picnics on the grass.

Bills now pending in Congress would require businesses to give unpaid leave to workers with a newborn, newly adopted or seriously ill child and provide home health care for the chronically ill.

The parental and medical leave legislation is opposed by many business groups, who object to federally mandated workplace benefits.

The Reagan administration also contends that such matters should be worked out between employers and employees, not ordered by Congress.

"Government was not created for defense alone," said Rep. Tony Coelho, D-Calif., the House majority whip. "This administration does not understand this message, for they are out of touch with the needs of everyday working Americans."

He told the crowd that passage of the bills would signal an end to the "long, national nightmare that has been the Reagan years."

"We know that our family and our future do not belong to Ronald Reagan and the right wing of the Republican Party," Coelho said. "To compete in this economy, our kids need more than a right wing and a prayer."

Lane Kirkland, president of the AFL-CIO, said the rally "celebrates the family values that are advanced and supported . . . by the whole American labor movement, men and women, mothers and fathers, sons and daughters and grandparents alike."

The House Education and Labor Committee last November approved a family and medical leave bill requiring firms with at least 50 employees to offer up to 10 weeks of unpaid leave over a two-year period to workers with a newborn, newly adopted or seriously ill child. Employees with serious medical conditions of their own would be entitled to up to 15 weeks of unpaid leave over a year's time. The House leadership has not yet scheduled floor action on the bill.

In the Senate, Sen. Christopher Dodd, D-Conn., is sponsoring a family leave bill that would require businesses with more than 15 employees to offer up to 18 weeks of unpaid leave upon the birth, adoption or serious illness of a child. Cost estimates by the General Accounting Office range from less than $500 million for the Dodd bill to less than $200 million for the House measure, a compromise worked out by Democrats and moderate Republicans. Business groups contend the costs would be higher.