NEW YORK (AP) _ The widow of the American killed by hijackers aboard an Italian cruise liner told President Reagan on Saturday that she spat in the faces of the terrorists in Italy, where she identifed the men for authorities.

Reagan, who telephoned to console Marilyn Klinghoffer, reportedly replied: ''You did? God bless you.''

The conversation was recounted by Letty Simon, a family spokeswoman appearing outside the Klinghoffer's Manhattan apartment, where Mrs. Klinghoffer arrived after a flight from Cairo, Egypt, to Newark, N.J., aboard an Air Force jet. Mrs. Klinghoffer, 58, remained inside.

''These people don't deserve to live,'' Mrs. Klinghoffer reportedly told Reagan. ''Last night in Italy, I had the opportunity to face every one of them and I spat in their faces and told them I hate them.''

She also told Reagan, ''I just want you to know how much the terrorists hate you.''

''I appreciate that,'' the president reportedly responded. ''I hope they will have more reason to hate me in the future.''

Mrs. Klinghoffer told Reagan, ''I will do anything I can'' to see that the killers of Leon Klinghoffer, 69, are brought to justice, said Ms. Simon.

Mark Weinberg, an assistant presidential press secretary, said, ''Mrs. Klinghoffer told the president how much she appreciated what he had done. She also told him she had an opportunity to face the four terrorists and she told them how despicable they are.''

Mrs. Klinghoffer and other Americans who were held hostage on the Achille Lauro stopped Saturday at Siracusa, Sicily, en route to the United States and identified the hijackers in a ''lineup,'' officials and relatives said.

U.S. warplanes intercepted an Egyptian jet carrying the hijackers and forced it to land in Sicily, where the terrorists were being held for trial.

At the sidewalk news conference here, Mrs. Klinghoffer's son-in-law, Jerry Arbittier, said ''the family is holding up well.''

''For the past two days, we really have not been able to mourn. We have been actively trying to secure the freedom of our mother and her friends. We would now like to go upstairs and mourn the way I would really like to,'' said Arbittier.

He said the family would be in seclusion for the next several days.

Asked whether Mrs. Klinghoffer would return to Italy to testify against the hijackers, he replied: ''Marilyn said, 'I want to get them 3/8 I want to get them. I will do anything to get them 3/8' ''

Charlotte Spiegel, who accompanied the Klinghoffers on their cruise, said Mrs. Klinghoffer did not learn her husband had been killed until the day after he was shot and thrown overboard along with the wheelchair to which he was confined because of a stroke.

Mrs. Speigel, also of New York City, said Klinghoffer was separated from the other hostages because his wheelchair would not fit through a passageway through which the terrorists led the other hostages.

''Leo couldn't go upstairs, so he had to be left behind. She heard the shots, but she didn't know they were for him,'' said Mrs. Spiegel.

She was ''told that he had had some sort of heart seizure and had been moved to the infirmary,'' said Mrs. Spiegel. She repeatedly asked to see him, but was not allowed. Finally, she asked a terrorist to check on him.

When the hijacker returned, Mrs. Spiegel said, he did not go up to Mrs. Klinghoffer but went to another corner of the room and looked worried.

It was not until after the hijackers had been removed from the vessel and the hostages freed that the captain broke the news to Mrs. Klinghoffer, said Mrs. Spiegel.