The Trumps made a brief visit to the Capitol rotunda, where Bush's flag-draped coffin was resting as part of tributes to honour the 41st US president and commemorate his extraordinary life.
Bush died peacefully Friday at age 94, at his home in Houston, a passing that led Americans to reflect on his life of duty and service to country as a leader of the so-called "Greatest Generation."
Only the second president to see his son follow him to the Oval Office, the Republican stalwart is being honoured with four days of commemorations and services in Washington and in Texas, where he will be buried Thursday.
Trump is scheduled to attend a state funeral service Wednesday at Washington National Cathedral -- the first presidential funeral since Gerald Ford died in 2006.
With the first lady at his side, Trump saluted, and they stood at Bush's casket for about a minute. They exited the rotunda with little fanfare.
Bush never warmed to Trump, and he had let it be known that he did not vote for him in 2016. Trump himself has criticized the elder Bush on the campaign trail.
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." "President Bush worked selflessly throughout his long life to bring about a world of justice and lasting peace," he wrote.
Bush was a decorated World War II fighter pilot, onetime ambassador to China, former head of the Central Intelligence Agency, and vice president to Ronald Reagan before winning the White House.
Military pallbearers carried the flag-draped casket into the rotunda as a fiery sunset bathed Washington in a glow.
"He kept us flying high and challenged us to fly higher still. And he did it with modesty and kindness that would have been surprising in someone one tenth as tough and accomplished as he was," he said.
Bush was transported aboard the presidential Boeing 747 -- made available at Trump's direction -- from Houston to Joint Base Andrews, in Maryland.
In Houston, relatives including his presidential son stood with hands on their hearts as the casket was carried to the aircraft.
Bush is the 12th US president to lie in state in the rotunda. Just three months earlier, the honor was accorded to senator John McCain, a former Republican presidential nominee who died of brain cancer.
Hundreds of members of the public began quietly filing in to the Capitol late Monday to pay their final respects.
Among them was Kim Frinzell, a government employee who did not vote for Bush but grew to respect his accomplishments, including signing the 1990 Americans with Disabilities Act. AFP
(With inputs from agencies.)