Former vice president Nelson A. Rockefeller will be buried Monday at a service for family members only, the Rockefeller family announced today.

Two memorial tributes, one in New York City and one in Albany, will be held later. Rockefeller, 70, suffered a fatal heart attack Friday night.

The three-time presidential candidate who was governor of New York for 15 years will be cremated and his ashes will be buried at 11 a.m. Monday in the Rockefeller family cemetery on its Pocantico Hills estate in Westchester County outside New York City.

On Friday, a memorial tribute "for family, associates, close personal friends and national and international public officials" will be held in New York's Riverside Church at 11 a.m., the family announced.

The Rev. Marshall L. Smith of Union Church in Pocantico will officate at the grave and Dr. William Sloan Coffin will preside at the memorial service.

The funeral and memorial plans apparently make it possible for President Carter to attend the memorial service. The timing will not pose a conflict for headlines between the tribute to Rockefeller and the elaborately ballyhooed visit of China's Vice Premier Teng Hsiao-ping who arrives in Washington today.

The second memorial service for Rockefeller, on a date not yet chosen, is being planned by Gov. Hugh Carey as a major NEW York tribute to the man who served the second-longest term as its governor.

Rockefeller's body was taken to a funeral home in Tarrytown, near the family estate, after he was pronounced dead at Lenox Hill Hospital in New York City.

Rockefeller collapsed in his first-floor office in a townhouse at 13 W. 54th St. at about 10:15 p.m. Friday, and apparently died instantly, family spokesman Hugh Morrow reported.

It was initially reported by Morrow that Rockefeller had suffered his heart attack in his 56th floor office at 30 Rockefeller Plaza. "Actually, the death occurred in Mr. Rockefeller's private office," Morrow said in a statement this afternoon. "the error was entirely mine."

The call to police was placed at 11:16 p.m. by Rockefeller's bodyguard. Police said the bodyguard and Rockefeller aide Megan Marshack were at the townhouse when two police officers arrived at 11:18 p.m. Efforts by the officers to revive Rockefeller failed and he was taken to Lenox Hill Hospital. Doctors said that he showed no signs of life when he arrived there at 12:06 a.m. today.

Dr. Ernest Easkof, Rockefeller's private physician, pronounced him dead at 12:20 a.m. and said deaths was caused by cardiac arrest.

Rockefeller had no serous illnesses during his long and vigorous public career. In 40 years, he liked to say, he missed only three days of work.

Morrow said the last day of Rockefeller's life was much like other recent days revolving around his giant art collection.

Rockefeller spent most of the day in his office working on a book he was writing about 20th century art. In late afternoon, he went to the Buckley School where his two youngest sons are students to introduce a speech by his long-time associate, former secretary of state Henry A. Kissinger. It was Rockefeller's last public appearance.

After dinner with his wife, Happy, and the two sons at their duplex apartment on Fifth Avenue, Rockefeller left to return to work on his book about 9 p.m., Morrow said.

Rockefeller had been writing about art and also promoting the sale of reproductions of his collection -- a venture that had brought him considerable criticism in the art world.

Despite charges that his expensive reproductions were essentially valueless and that people would be better advised to buy smaller originals by the same artists or originals by lesser-known artists, Rockefeller had planned to announce today that his retail outlet for the reproductions in New York was becoming a permanent store because of the encouraging response in its first months of operation. He was scheduled to make that announcement in a speech to the World Antiques Market Conference here.