Citizens and politicians who never met Leon Klinghoffer and a cousin who knew him as a "shy and modest man" came together yesterday for a moving memorial service on the lawns of the U.S. Capitol and sent out the message that his slaying by Arab hijackers has signaled a new beginning in the fight against terrorism.

"Just as Anne Frank became a symbol of victory over the Nazis, Leon Klinghoffer will become a symbol of victory over terrorism -- a catalyst for a new beginning, for a world without fear and without terror," said Sharon Hellman, cousin of the 69-year-old stroke victim who was slain on the Achille Lauro cruise ship and dumped overboard with his wheelchair.

Over and over during the hour of speeches, senators and congressmen, citizens and clergymen expressed their belief that Klinghoffer's death was not -- and must not be -- in vain. Along with their outrage, they poured out a newfound sense of pride, born of the dramatic U.S. capture of the four alleged hijackers.

"We fervently hope that these actions have turned the tide on terrorism," said Rochelle Herman, a Bethesda physician who initiated plans for the service.

Sen. Alfonse M. D'Amato (R-N.Y.) said he and other senators have called on the secretary of state to post a $500,000 international reward for the capture of Mohammed Abbas, who has been charged with masterminding the hijacking.

D'Amato also denounced Egyptian President Hosni Mubarak for releasing the hijackers. Rep. Bill Green (R-N.Y.) called for Congress to cut its $2 billion aid package to Egypt.

Still, it was not a day for politics. It was a day for emotion, for remembering the man who was shot by terrorists, then dumped overboard -- "like trash from the fantail of a ship," as one clergyman said.

That act -- and pent-up frustration over unavenged bombings, hijackings, kidnapings and slayings -- galvanized Americans, including three suburban Maryland residents who never knew the Klinghoffer family but knew that they must do something to mark Klinghoffer's death.

"We got together and said, 'We've had enough. This can't go on,' " said Fred Schulman, a Silver Spring businessman who was one of the three. Out of their meeting came yesterday's ceremony, drawing dozens of spectators and a horde of reporters.

This time reaction was different than it had been to the hijacking of the TWA plane during the summer or the 1983 Beirut bombing that killed 241 servicemen, several speakers said.

"Finally, the world . . . has come to see the horror of that kind of terrorist activity," said Rep. Ted Weiss (D-N.Y.).

Green said, "It has taught the world a lesson -- that people who shoot a helpless, unarmed old man in a wheelchair are not patriots. They're not heroes. They're not freedom fighters. They're just plain murderers, and brutal ones at that."

Sen. Frank R. Lautenberg (D-N.J.) spoke of the hijackers' capture. "For too long now, we have seen terrorists run rampant . . . with nothing more than words to fight back. This time we had a chance to strike back."

President Reagan sent a message, expressing his grief and his prayers. "Terrorism," it said, "is one of the great tragedies of this world."

Hellman's words brought that tragedy home. Her cousin, she said, was a "gentle and compassionate" man, who "worked 90 hours a week so his family could have the things he couldn't have" when he was young. "He was a fighter, in his quiet, very humble manner," she said, who taught himself to speak and to write with his left hand after two strokes paralyzed him. "This shy and modest man, catapulted by world outrage, would never have envisioned the role history has cast him in," she said.

Lillian Gechter, an elderly woman in the crowd, came to touch Hellman's hand after the ceremony ended. "He gave his life for something from which good for others may come," Gechter told her. "Maybe he saved other lives."