Marilyn Klinghoffer, whose husband Leon was murdered in the hijacking of the Achille Lauro and who began a campaign to enlist citizens as "foot soldiers in the battle against terrorism," died of cancer yesterday in a New York hospital. She was 59.

A family spokesman, Letty Simon, said that Mrs. Klinghoffer died at about 5 a.m. at Lenox Hill Hospital, with her children and other family members present. Her daughters, Ilsa Klinghoffer and Lisa Arbittier, are in seclusion, Simon said.

Leon Klinghoffer, 69, was shot as he sat in his wheelchair and his body dumped overboard when Palestinian hijackers seized the Italian cruiseliner last Oct. 7 as it sailed the Mediterranean off Port Said, Egypt. His body eventually washed ashore on the coast of Syria.

Simon said that the Klinghoffers were aware of her condition at the time of the cruise. "It was diagnosed in the fall of 1984," she said. She declined to say what type of cancer Klinghoffer had.

Simon said that Mrs. Klinghoffer's condition did not prevent the trip, in celebration of the couple's 36th wedding anniversary, from being a pleasant vacation until the four hijackers took over the ship.

"I think she and Leon were able to enjoy it at the time," Simon said. "It was the trip of a lifetime."

Last week, Simon announced that Klinghoffer had sold the story of her husband's death to a production company for a television movie. Klinghoffer, who had worked as assistant personnel manager at a business and trade publishing company in New York, was to have been a consultant on the production. No mention was made of her illness at that time.

Simon said that the Klinghoffer children will propose that the Leon Klinghoffer Foundation, begun by Mrs. Klinghoffer, be renamed the Leon and Marilyn Klinghoffer Foundation. The foundation has collected $25,000 to $50,000, Simon said, mostly in small donations, and a decision will be made later on how to use it in the battle against worldwide terrorism.

The four accused hijackers were captured when U.S. Navy planes forced an Egyptian airliner to land at a North Atlantic Treaty Organization base in Sicily, but Italian troops prevented U.S. troops from removing them from Italian soil. The four were convicted in Italian court on weapons charges and await trial on charges of hijacking and murder.

Klinghoffer, shortly after the hijacking, met President Reagan and told him she spat in the faces of the terrorists as she identified them in Italy, and Reagan said, "God bless you." She had vowed to go to Italy or anywhere else to testify against the "cold-blooded murderers, liars and cowards" who killed her husband.

Klinghoffer told reporters that the 11 Americans and six British citizens aboard the ship were separated from the rest of the passengers and ordered to climb a narrow staircase.

"I attempted to push my husband in his wheelchair in the direction of the staircase," she said. "The terrorists ordered me to leave him. I told them that I couldn't leave him and begged them to let me stay with him. They responded by putting a machine gun to my head and ordered me up the stairs. That was the last time I saw my husband."

She testified at a House Foreign Relations subcommittee on Oct. 30 that what happened on the Achille Lauro "could happen to anyone at any time and at any place." She endorsed an international conference on terrorism.

"I believe my husband's death has made a difference in the way that people now perceive their vulnerability," she testified.

On Nov. 27, she filed a $1.5 billion suit in a New York court against the Palestine Liberation Organization and another seeking an undetermined amount of money from the owner of the ship, the Italian port of Genoa where the ship was based and the travel agency that arranged the tour.

The White House issued a statement yesterday saying, "Mrs. Klinghoffer was a courageous woman who stood for her principles in speaking out eloquently against terrorism. The president will be sending his condolences to the family."