Bush broke down briefly at the end of his eulogy while invoking the daughter his parents lost when she was 3 and his mother, Barbara, who died in April. Trump then saluted Bush, a gesture belying the history of antipathy between the Republican president and the Bush family. He arrived in the Capitol rotunda in a wheelchair pushed by an aide.
From 6:45 pm until Thursday at 6 am, the public is invited to pay their final respects to President Bush as his body lies in repose.
The United States flag is lowered to half mast aboard USS George H.W. Bush on December 1, 2018.
The patriarch of the Bush family served as a fighter pilot during World War II, later being elected to Congress, serving as United Nations ambassador, Central Intelligence Agency director, vice president under Ronald Reagan between 1981 and 1989 and finally being elected president and serving for one term from 1989-1993 during which time he presided over the end of the Cold War and launched the Gulf War to drive invading Iraqi forces under dictator Saddam Hussein out of Kuwait.
But on Monday, Trump wrote members of Congress to hail Bush as a man who "led a life that exemplified what is truly great about America".
The Trumps made a brief visit to the Capitol rotunda, where Bush's flag-draped coffin was resting as part of tributes to honor the 41st USA president and remember his extraordinary life. Service dogs are trained to do that.More news: Saudi US embassy road could be renamed 'Jamal Khashoggi Way'
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"He was the first president to teach me that in a democracy sometimes you fall short - and that how you handle that is just as important as how you win", Ryan said.
National flags flew at half-staff on many foreign diplomatic buildings on Washington's "Embassy Row", past which Bush's coffin will be transported on its way to the Washington National Cathedral for a memorial service on Wednesday.
Bush was elected president in 1988 after serving two terms as President Ronald Reagan's vice president.
Bush's service dog, a young Labrador retriever named "Sully", also walked past the casket and sat near it briefly. John McCain was the last public figure to lie in state there.
"We'll be spending three days of mourning and three days of celebrating a really great man's life", Trump said in Argentina where he was attending the G20 summit.