Patricia Roberts Harris, a dining car waiter's daughter who as a lawyer, diplomat and Cabinet secretary spent much of her life breaking longstanding barriers to black women, died of breast cancer yesterday at George Washington University Hospital. She was 60.

Harris had been treated for cancer for more than a year, and a hospital spokeswoman said she was last admitted to the hospital on Wednesday.

Possessed of a tough, honest and demanding intellect, Mrs. Harris came to Washington as a college student and spent most of her career here achieving "firsts." She was the first black woman in the Cabinet, serving as secretary of Housing and Urban Development and then as secretary of Health, Education and Welfare during the Carter administration, the first black woman to become an ambassador or to become dean of a law school, and the first American black to serve as a delegate to the United Nations.

In 1982, she ran unsuccessfully for mayor of her adopted home town, losing to Marion Barry in the District's Democratic primary. Since then she had been a professor at George Washington University National Law Center.

"When you think of a woman, a black woman born in 1924 in Mattoon, Ill., who moved to such heights and achieved such incredible firsts, made such extraordinary contributions to the nation, and paved the way for so many women, particularly black women, then you can understand that hers was not an easy row to hoe . . . . She leaves an incredible legacy," said Sharon Pratt Dixon, treasurer of the Democratic National Committee and manager of Mrs. Harris' campaign for mayor.

Former president Jimmy Carter said yesterday from his home in Plains, Ga.: "She was a fine lady and a fine Cabinet officer, sensitive to the needs of others. She was an able administrator and an inspiration to me and to everyone who knew her."

Mayor Barry said yesterday that his one-time opponent "made a great contribution to this society."

Mrs. Harris' death came five months after her husband of 29 years, William B. Harris, an adminstrative law judge with the Federal Maritime Commission, died at age 70.

A complex, extremely private person who bristled at mediocrity, Mrs. Harris was renowned for upbraiding subordinates who failed to meet her uncompromising standard of excellence.

"She always impressed me as someone who cared very much about people who were not getting a decent shake, and she also impressed me as being tough as nails when it came to taking care of their interests," said Jody Powell, Carter's presidential press secretary. "I was occasionally on the other side of White House arguments with Pat Harris, and there was nothing I dreaded more than going up against her . . . , but one of the privileges of serving in government is the people you meet, and I count as a great privilege having been able to know Pat Harris."

Mrs. Harris' insistence on excellence also put her at odds with some blacks during the height of the civil rights movement in the late 1960s. When students at Howard University School of Law were demanding elimination of letter grades and striking for student control of the school in 1969, Mrs. Harris, then the dean, maintained an unyielding position. She said the law school's purpose was to produce "the very finest lawyers," and she would not be party to diluting that purpose. She later resigned after charging that the university president, James Nabrit, had undercut her by privately negotiating with the students.

Similarly, during the congressional hearings to confirm her as HUD secretary in 1977, she was accused of holding a series of establishment jobs during the 1960s protests when other blacks were involved in demonstrations and sit-ins. Mrs. Harris did not brook the criticism politely.

Appearing before the Senate Banking Committee, she was pressed by Sen. William Proxmire (D-Wis.) as to whether she had empathy for the poor.

"Senator I am one of them," she replied. "You do not seem to understand who I am. I am a black woman, the daughter of a dining car worker. I am a black woman who could not buy a house eight years ago in parts of the District of Columbia . . . . If you think I have forgotten that, you are dead wrong."

When the same line of criticism emerged during her campaign for mayor of Washington, she pointed out that she had led civil rights demonstrations when the city was rigidly segregated, successfully integrating the Little Palace Cafeteria at 14th and U streets NW in 1943.

"Oh, they weren't on the front lines," Harris said of critics who said she had not been in the 1960s demonstrations like some other Washington activists. "They were there when it was safe, when the television cameras were there. I was there when there were no television cameras."

"Way back, I started out as a Pat Harris opponent," said R. Calvin Lockridge, the Ward 8 school board member who supported Mrs. Harris' mayoral bid. "It took me a long time to understand her role as a catalyst inside the system who would never compromise her position for the people she identified with."

"Some would say she was not warm enough," said Randy Kinder, who was executive assistant to Mrs. Harris at HEW and later when it became the Department of Health and Human Services. "That's because she was never in the self-promotion business. She was not one to go around pleasing people, in or out of the government, and telling them things were okay when nothing was okay.

During her tenure at HUD, subsidized housing starts quadrupled, and she started the highly successful Urban Development Action Grant (UDAG) program, which spurred private investment in decaying cites and was responsible for projects such as Baltimore's Harborplace.

Her most notable work at HEW was her protection of social programs during a period of budget cutting. At a time when support for social programs was dwindling, she won a $25 billion increase for the department's budget.

Half of her political appointees at HUD were women, and 28 percent were blacks or Hispanics. At HHS 67 percent of her appointees were women and minorities.

Despite her proven record of success, the hard edge to her personality proved a liability when she campaigned for mayor, and she won only 36 percent of the primary vote.

"I think people who are very bright like Pat, super-intelligent people who have a sense of vision, naturally are bad campaigners," said William Lucy, a labor official who backed Mrs. Harris for mayor.

Mrs. Harris was the daughter of Hildren and Bert Fitzgerald Roberts, who separated when she was 6 years old. She grew up in Chicago, and her family, hard-working Episcopalians, put a premium on education, success and upward mobility, Mrs. Harris recalled in an interview during her mayoral race.

"She was a wonderful daughter, always studious, always hard-working and ambitious," her mother said yesterday. "She started studying hard at age 3 and never stopped."

Mrs. Harris graduated with honors from Howard University in 1945 and did graduate work at the University of Chicago. She worked in Chicago for the YWCA before returning to Washington, where for more than a decade she was involved in civil rights and social work through the American Council on Human Rights and Delta Sigma Theta, a black sorority.

She graduated first in her class from George Washington law school, and, after a brief stint at the Justice Department, returned to Howard to teach law, eventually becoming dean. At the 1964 Democratic National Convention she seconded the presidential nomination of Lyndon Johnson, and the next year Johnson appointed her ambassador to Luxembourg.

After resigning as Howard law dean, she was a partner in the law firm of Fried, Frank, Shriver and Kampelman until 1977, when President Carter appointed her to HUD.

She is survived by her mother, of Chicago.