Sully the service dog, famously photographed laying in front of President George H.W. Bush's casket, will return to work shortly after the death of his owner, but this time with others who desperately needs him. Once steadied, Mr Dole saluted.
Mr Trump repeatedly criticised Mr Bush Jnr's policies, not least his Middle Eastern military intervention, and defeated Jeb Bush, his brother, in the 2016 race for the Republican presidential nomination, dubbing him "low-energy Jeb".
Bush died on Friday at age 94.
Mr Bush is lying in state at the Capitol until the Washington National Cathedral service.
President Donald Trump has designated today as a national day of mourning for former President George H.W. Bush, who died November 30. The late President Bush called Trump a "blowhard".
Bush then continued down the row, shaking hands with former president Bill Clinton, former First Lady Hillary Clinton, former president Jimmy Carter and his wife, Rosalynn.
Trumps, Obamas, and Clintons’ Greetings Include ‘Cold Shoulder’ At Bush Funeral
An aide helped Dole to his feet and supported him as he raised his left hand in salute to the flag-draped casket . Bush's death reduces membership in the ex-presidents' club to four: Jimmy Carter, Bill Clinton , George W.
Trump, the day before, spent 20 minutes visiting Bush family members, who were staying at Blair House, across the street from the White House. Among them was the former US President's prominent friend - Sully, his service dog.
In an invocation opening proceedings, the US House chaplain, the Reverend Patrick J Conroy, praised Mr Bush's commitment to public service, from Navy pilot to congressman, United Nations ambassador, envoy to China and then Central Intelligence Agency director before being elected vice-president and then president - the first incumbent to do so in over 100 years.
4, Clarence House tweeted, "The Prince of Wales will attend the state funeral of former U.S. President George H.W. Bush".
A Connecticut Yankee from a wealthy family who moved to Texas to be an oilman, Bush has been eulogized as a president with a keen sense of civility and duty.
Although Bush's funeral services are suffused with the flourishes accorded presidents, by his choice they will not include a formal funeral procession through downtown Washington.
The New York Stock Exchange, as well as the NASDAQ, will also be closed.