Demonstrations against apartheid continued yesterday at the South African Embassy here and in several other cities while organizers of the Free South Africa Movement said they are discussing ways to spread the protest abroad.

The Rev. Daniel Berrigan and author Michael Harrington, cochairman of the Democratic Socialists of America, were arrested in New York during demonstrations at the South African consulate.

In the District, Rep. Louis Stokes (D-Ohio), chairman of the House ethics committee; Judy Goldsmith, president of the National Organization for Women, and Evelyn Lowery, representing the women's division of the Southern Christian Leadership Conference, were arrested for demonstrating within 500 feet of the embassy.

In Boston, two other demonstrators, including a local City Council member, were arrested in the offices of a gold exchange firm that markets South African gold coins.

Actor Tony Randall, a founder of the year-old Artists and Athletes Against Apartheid, joined picketers at the embassy protest here, saying the campaign against apartheid had "taken off like wildfire."

Noting existing antiapartheid groups in England, the Netherlands, France and Africa, D.C. Del. Walter E. Fauntroy said leaders are exploring ways to combine forces. Also, he said, churches in this country are being called on to designate Dec. 23 as Free South Africa Sunday.