"The President will designate Wednesday, December 5th as a National Day of Mourning".
Trump's mockery drew condemnation from the extended Bush political family. "We salute this great American leader, who challenged us to chart a course for the future to benefit all humanity".
Mr Bush was inaugurated president from the Republican Party, having been Ronald Reagan's Vice President throughouth both the latter's terms, in January 1989 to January 1993, after losing the election to Bill Clinton (D).
Additionally, Trump will speak with former President George W. Bush on Saturday morning to offer his condolences.
He added, "President Bush always found a way to set the bar higher".
"With sound judgement, common sense and unflappable leadership, President Bush guided our nation, and the world, to a peaceful and victorious conclusion of the Cold War". He was an honorable, gracious and decent man who believed in the United States, our Constitution, our institutions and our shared future.
A funeral service is planned for Washington's National Cathedral.
"It is with great sadness that we mark the passing of one of America's greatest points of light", Trump said in a statement.
"President Bush inspired generations of his fellow Americans to public service - to be, in his words, "a thousand points of light" illuminating the greatness, hope, and opportunity of America to the world."
Trump, who upended the GOP establishment with his insurgent presidential campaign, has had a fractious relationship with the Bush family over the years.
Bush, the 41st president of the United States, lived longer than any of his predecessors. But he made clear what he thought of Trump.
Bush first met with church leaders in 1982 while vice president. "Since George's mother called Grandfather Walker "Pop, ' she began calling her son, his namesake, 'little Pop, ' or 'Poppy" Hence, Poppy Bush is the name the President's family friends have called him since his youth", the book says.