A Catholic bishop and a Nobel laureate in medicine were arrested yesterday at antiapartheid protests in New York and Boston as the "Free South Africa" movement widened its sweep into the nation's financial centers.

The Boston arrests, the first at demonstrations there, followed by one day the resignation of South Africa's honorary consul in that city and signalled a new phase of the protests aimed at halting the sale of South African gold Krugerrands in this country.

The demonstration at the Boston offices of Deak-Perrara Inc. took place as four persons met with representatives of the nation's largest currency exchange to ask that sale of Krugerrands be suspended until South Africa changes its policy toward its black majority.

When company officials said they would not stop trading in the gold coin, the four -- including Boston City Council member Bruce Bolling and 78-year-old Dr. George Wald, who won the 1967 Nobel Prize for medicine -- refused to leave and were charged with trespassing.

In Washington, as protests here marked their 15th day, the leadership of the movement expressed a renewed solidarity as they mended a threatened rift over the Rev. Jesse S. Jackson's planned trip to South Africa next month.

Emerging from a Capitol Hill meeting with 10 members of the Congressional Black Caucus, Jackson said protest leaders -- who had expressed concern that the journey would divert attention from their cause -- had given him their blessing.

A few hours later, Reps. William L. Clay (D-Mo.) and Robert Garcia (D-N.Y.) and William Lucy, secretary-treasurer of the 1.1 million-member American Federation of State, County and Municipal Employees, became the latest persons to be arrested here. Twenty-five people have been arrested here since the protests were launched Nov. 21.

Meanwhile, White House officials said yesterday that President Reagan will meet privately this week with Bishop Desmond Tutu, the South African Nobel Peace Prize winner who has called administration policy toward his country "immoral, evil and totally unchristian."

In New York City, five more demonstrators, including Bishop Emerson Moore, were arrested, and in Los Angeles, movement supporters said they were exploring ways to support economic sanctions that would "go beyond the impact" of protesters going to jail.

On the Hill, 35 conservative Republican members of Congress handed the South African ambassador the news that they will support diplomatic and economic sanctions against his country unless immediate steps are taken to end apartheid.

Jackson also traveled to the Hill for his meeting with members of the Congressional Black Caucus. Jackson left the meeting, saying that no one who attended had asked him to cancel his trip to South Africa.

"We are concerned by any attempt to use us for diverting attention" from the movement, Jackson told reporters. "There are many roles but one goal."

Sources close to D.C. Del. Walter E. Fauntroy, a top movement leader, had said Tuesday that members of Congress would urge Jackson to cancel what they see as a grandstanding trip.

But Fauntroy said yesterday, "We have not had any question about his going to South Africa . . . We are working to make sure conditions of the trip will enhance the movement here and around the world."

In Boston, South Africa's honorary consul, attorney Richard K. Blankstein, resigned Tuesday after a visit by three protesters. Blankstein asserted in his resignation letter that he did not "choose to be a spokesman or apologist for the government of South Africa," according to movement supporters. Blankstein refused through a receptionist to comment.

Blankstein is one of South Africa's eight "honorary consuls," Americans who, according to an embassy spokesman, serve as liaisons for U.S. business firms and banks and help people in their cities who want to travel to South Africa.

These consuls are located in Boston, Mobile, Salt Lake City, Portland, Ore., Phoenix, New Orleans, Seattle and Cleveland. They do not have the same powers as officials in the four consulates in New York, Chicago, Houston and Los Angeles, which are suboffices of the embassy and can issue visas or help South African citizens with problems they encounter in the United States, the embassy spokesman said.

Still, demonstrators have knocked at the honorary consuls' doors in several cities, attempting to pressure these Americans to stop representing the interests of South Africa while that country practices its segregationist policy of apartheid.

Meanwhile, the arrests outside the embassy on Massachusetts Avenue NW, which have become daily rituals, continued, but with a new twist. Usually, protesters are arrested after knocking on the embassy door in an effort to see the ambassador, and then when the door is not opened, walking to the sidewalk to sing a protest song.

On Tuesday, because the embassy was closed at the time of the protest, demonstrators were arrested just after crossing police lines, set up 500 feet from the embassy. It is illegal to congregate and demonstrate any closer to a foreign embassy's door.

Sources at TransAfrica, the lobbying group organizing the protest, said leaders were unhappy with that arrest, far from the embassy's door. So, yesterday, three soon-to-be-arrested protesters jumped into the waiting car of Fauntroy, which drove them around the police line and to the embassy's front door.

However, the three apparently were not briefed on arrest protocol -- the fact that they had to make some verbal form of protest to break the law.

Both police and the silent protesters stood their ground for 30 minutes in the driving rain, until an organizer drove by and yelled "Sing! Sing!" The three on the doorstep started to laugh, sang a verse of "We Shall Overcome," and were then arrested and charged with congregating within 500 feet of an embassy with intent to demonstrate.

Police said the three were later released on their own recognizance. It was the first time since the protest began that none of those arrested chose to spend a night in jail.