Mr. Bush has been lying in repose at St. Martin's Episcopal Church, where his family worshipped. The family took up their seats on the opposite side of the aisle to President Trump and the former presidents.
The passing of Bush, only the second president to see his son follow him to the Oval Office, has led Americans to reflect on his life of duty and service to country as a leader of the so-called "Greatest Generation".
Alan Simpson, former Republican senator from Wyoming, regaled the congregation with stories from his years as Bush's friend in Washington. The Clintons looked directly ahead and did not acknowledge the Trumps.
As IJR previously reported, Trump had an awkward entrance into the state funeral for Bush when he was seated next to several people that he wasn't on the best of terms with, including former President Barack Obama and his former opponent, Hillary Clinton.
But at virtually every turn, in every rhetorical flourish hailing the elder Bush as a paragon of leadership, virtue and character, the contrast and the tension were palpable.
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Wednesday's state funeral caps a day-long homage that saw Bush lie in state for two days in the US Capitol rotunda. Then-Vice President Bush was a big fan of the group, and through the years they became friends. Former first lady Laura Bush wiped her eyes with a tissue as her husband sat next to her.
The nation's 41st president died last week at age 94. Lemon said, referring to footage of Trump and the Obamas shaking hands. The funeral of former President Ronald Reagan in 2004 brought together both Bushes, Clinton, Carter and Gerald Ford.
"Even someone as modest as me", he said, pausing for a cascade of knowing laughter, "threw in a few more adjectives here and there, to extend the pleasure of the experience".
Following the funeral at St Martin's, where Bush and his late wife, Barbara Bush, were long-time worshippers, a train will carry his remains about 100 miles (160 km) northwest to College Station, Texas, where he will be laid to rest at his presidential library.
Former President George W Bush wipes his eye at the State Funeral for his father.