Those attending a funeral mass in Maryland included his daughter, former reporter Maria Shriver; her husband, former California Gov. Arnold Schwarzenegger; Vice President Joe Biden; and former President Bill Clinton.
Shriver, who was Democratic presidential nominee George McGovern's 1972 running-mate, died Tuesday at the age of 95.
The founder and first director of the Peace Corps had been president of the Chicago Board of Education.
Maria Shriver also spoke, saying her family took comfort in "knowing that Daddy is in heaven with God and Mummy," referring to her mother, Special Olympics founder Eunice Kennedy Shriver.
"For me, as his only daughter, perhaps his greatest achievement was showing us, in our family, how to show up in other people's lives, and how to love unconditionally," Maria Shriver said.
Tim Shriver said Saturday during his father's funeral service that Sargent Shriver saw the world as "infused with God's spirit." He says his father never coddled his children and encouraged them to pursue big ideas. He told those gathered: "I hope you, too, will carry a little 'Sarge' in you."
First Lady Michelle Obama was among the mourners.
The Associated Press contributed to this report.