Mr Bush had passed Mrs Obama a cough drop when they were seated next to each other at Senator John McCain's memorial service in September.
His casket is now lying in state and will remain there until Wednesday morning when it will be transferred to the National Cathedral for the funeral.
Vice President Mike Pence and Republican Senate leader Mitch McConnell also spoke.
"He left a simple, yet profound legacy to his children, to his grandchildren and to his country: service", George P. Bush said.
Bush achieved the office that Dole sought in 1996 as the Republican presidential nominee.
The service began at St. Martin's Episcopal Church, where Bush worshipped for more than 50 years, with more than 1,000 attendees singing "America the attractive".
A state funeral for George H.W. Bush will be held at the National Cathedral in Washington, D.C on 5 December, followed by a funeral service in Texas where America's 41st President will be laid to rest.
Bush, who died Friday at the age of 94, will be memorialized on Wednesday at the National Cathedral in Washington.
We'll need a few options to take down Kohli Hazlewood
For the 30-year-old Pujara, the looming Test series is a chance to rectify one blot on his impressive cricketing resume. Paine expressed confidence that the four-bowler attack will get through the four Tests without any fitness concerns.
President Donald Trump tweeted earlier Tuesday that Mrs.
Bush was president from 1989 to 1993, a time in which communism toppled across Eastern Europe and Walesa became president of a democratic Poland.
After Thursday's private services, the former president will be taken by a train, pulled by an engine commissioned in his honor, 120 kilometers north to the city of College Station for burial at his presidential library on the grounds of Texas A&M University. In place of most federal dignitaries were top Houston athletes including the NFL Texans' defensive end J.J. Watt - displaying Bush's love for sports - and Chuck Norris, who played TV's Walker, Texas Ranger.
George W Bush himself seemed to be holding back tears.
Pound drops to 2017 lows after government contempt vote
But it does highlight how little control May's fragile minority government has over MPs ahead of next Tuesday crucial vote . They may try to alter or delay Brexit, or derail it altogether, but her team is sticking to the script.
"I think he was one of the kindest, most generous men", said Marge Frazier, who visited the downtown statue Sunday while showing friends from California around.
Flags on public buildings are flying at half-staff for 30 days.
"Mourners laughed as Baker recalled how Bush would let him know a conversation was over: "'Baker, if you're so smart, why am I president and you're not?'" His voice cracking at moments, Baker said he was at his friend's deathbed last week.
The life of George Bush Senior
Gorbachev, 87, expressed his "deep condolences" to the family of the 41st U.S. president and the entire American nation. As he accepted the Republican Party's nomination for president in 1988, Bush pleaded for a "kinder, gentler nation".
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