The Trumps were informed of Mr Bush's death at the age 94 late on Friday while in Buenos Aires, Argentina, for the Group of 20 summit of rich and developing nations.
"President Bush is a personal hero of mine and a major inspiration in my life".
A funeral service is planned for Washington's National Cathedral. "Heartfelt condolences to the Bush family and to all Americans".
Bush first met with church leaders in 1982 while vice president. "And I'm not too excited about him being a leader".
"President Bush exemplified a lifetime of service to America as a World War Two combat pilot and during his tenure in public service".
President George H.W Bush was a devoted American with visions and will.
Michael Dukakis waves to the audience during the Democratic National Convention in Atlanta
The proclamation hails Bush as "one of America's greatest points of light", a reference to one of the former leader's signature phrases about the impact of American civic culture.
In an interview with NPR, Colin Powell, who served as chairman of the Joint Chiefs of Staff under Bush, called the former commander in chief "the most qualified president to take over that office in our history". As President, he saw the fall of the Berlin Wall and the collapse of the Soviet Union.
It was unclear whether the funeral of Bush - who as a genteel, New England-bred patrician was more restrained in his criticism of Trump than the outspoken McCain - would carry the same tone, especially considering Trump will be in attendance.
President Ezra Taft Benson and President Thomas S. Monson attended Bush's inauguration in 1989 and the Tabernacle Choir at Temple Square, then known as the Mormon Tabernacle Choir, sang. "His passion was a deep love of family and country".
Hume said that even as kind as Bush was "he had steel in him".