Trump and First Lady Melania met for about 20 minutes with the 43rd president and his wife, Laura, at the Blair House, a historic home across the street from the White House that traditionally houses the American president's guests.
None of them made statements to the press about the meeting, but Trump had tweeted on his official account that he would meet "with the wonderful Bush family" before the funeral.
The current first lady greeted former President Bush with two kisses on the cheek, and then the four entered the building.
The US president has avoided any controversy after the death of George W. Bush's father on November 30, even though over the past two years he has repeatedly criticized the two former presidents.
Trump will attend the former president's state funeral in Washington's National Cathedral on Wednesday, which is expected to be attended by the four living former US Presidents: Democrats Barack Obama, Bill Clinton and Jimmy Carter; and the Republican George W. Bush, who will deliver the eulogy.
After the funeral, the coffin of the former president will be transferred to Texas again, to receive a final farewell from his family on Thursday.
The remains of George H.W. Bush will rest together with "the love of his life", as he always defined his wife Barbara Bush, in the Bush Library located in College Station, Texas, some 160 kilometres from Houston.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)