Members of Congress and the Trump administration gathered near the flag-draped casket of George HW Bush in the centre of the US Capitol rotunda on Tuesday, joining the family and former members of the 41st US president's cabinet to recall his decency and lifetime of service.

Bush, who died Friday at age 94, was remembered for his kindness, his steady hand in leading the country at the end of the Cold War, his military service during World War II and his roles as US ambassador to the United Nations and head of the CIA.

"There was a kindness about the man that was evident to everyone who ever met him," Vice President Mike Pence said. Pence added that the Texan's years in public service were marked by modesty, noting he never penned an autobiography.

Bush opted instead to leave a written record in letters to loved-ones, especially his wife Barbara, who died in April, other politicians and just about anyone who took the time to write to him, Pence said.

Pence said that earlier this year after his son, a Marine aviator, made his first landing on the aircraft carrier named after Bush, he wrote to ask the former president to sign a photo of the ship. Pence said he was not surprised when Bush responded not only by signing the photo, but with a personal letter to his son.

"Though we have not met, I share the pride your father has for you during this momentous occasion," Bush wrote. "Wish you many CAVU days ahead."

Pence explained that CAVU stands for 'ceiling and visibility unlimited,' a term since Bush himself was a navy aviator to describe the kind of weather pilots wish for when they fly off aircraft carriers.

"That may well describe the essence of this man, and it may well be the vision that he had for his life and the lives of his family and his country - no barriers, no boundaries, no limits," Pence said.

"His example will always inspire and his lifetime of service will be enshrined in the hearts of the American people forever."

Pence expressed condolences on behalf of the Trump administration to the Bush family members present, including George W Bush, the 43rd US president, his brother Jeb Bush, a presidential candidate in 2016, and their siblings.

Trump, who sparred verbally with Jeb Bush during the campaign, did not attend the ceremony, which concluded with congressional leaders placing wreaths around the casket and beginning a procession of mourners.

Trump and his wife Melania paid their respects later on Monday.

The president and first lady entered the rotunda at 8:30 pm (0130 GMT).

Trump wore a dark overcoat over a suit, while Melania was dressed in a black outfit topped with a black coat.

They stood side by side for a minute in front of the casket, before Trump saluted the coffin. At the same time, Melania placed her hand on her heart.

Neither of them spoke. They left about two minutes after having entered the rotunda.

The day's events, which began earlier Monday at Bush's home in Houston, Texas, began a four-day period of mourning for the former US president, whose state funeral will be held Wednesday.

Bush's body arrived in Washington on a 747 jet that had been temporarily recommissioned "Special Air Mission 41" for the flight. His service dog Sully, a 2-year-old Labrador retriever, accompanied the casket and dozens of mourners.

The state funeral, which Trump along with several former presidents and high-ranking politicians are expected to attend, is scheduled to take place at Washington National Cathedral.

Bush's body will be flown back to Texas on Thursday for burial alongside his wife.