Bush died last week at the age of 94.
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As to why President Trump would not be giving the eulogy at his father's funeral, the former Florida governor said that it was a matter of circumstance, being that his brother is a former president.
The group had been friends with Bush since they played at a White House barbecue when Bush was vice president.
Representing Britain was Prince Charles and former British Prime Minister John Major, who was in office during Bush's presidency.
Watch a livestream of Thursday's funeral below, when it is available.
Her grandfather, she said, was heartbroken when his wife of 73 years died. A WWII combat veteran, Bush served as a member of Congress from Texas, ambassador to the United Nations, director of the Central Intelligence Agency, vice president and 41st president of the United States.
"As he aged, he taught us how to grow with dignity, humor, and kindness", Bush said.
Bush choked up at the end of his eulogy before regaining his composure.
He was one of the five living United States commanders in chief at the event; Jimmy Carter, Bill Clinton, Barack Obama all attended along with President Donald Trump.
Both the Trump and the Bush families have been all class in the wake of the 41st president's passing.
As the 72-year-old Bush arrived at the National Cathedral for the state funeral for his father - the 41st U.S. president - he shook hands with President Donald Trump and his wife Melania.
The congregation, filled with foreign leaders and diplomats, Americans of high office and others touched by Bush's life, rose for the arrival of the casket, accompanied by clergy of faiths from around the world.
The train will take his casket, family and closest friends about 70 miles to College Station, where Bush will be buried later Thursday during a private service at his presidential library. Trump and his wife took their seats after the others, briefly greeting the Obamas seated next to them. "I don't think anybody behaved badly", he said, recalling the bitter 2016 campaign between the two.
At a time of extraordinary and deep political fissures, Bush was looked to this week as a gracious, humble servant of country who aimed to bridge the divide.
The state funeral of the late president which is taking place at the Washington National Cathedral today has seen many political figures arrive to pay their respects.