Later, he will lie in state at the U.S. Capitol.
House Speaker Paul Ryan and Senate leader Mitch McConnell, both Republicans, also spoke.
Vice President Mike Pence has offered the nation's condolences to the family of the late former President George H.W. Bush.
Bush's casket is set to arrive in Washington on Monday afternoon aboard the US military airplane that's more commonly recognized as Air Force One.
Former President George W. Bush, Laura Bush, former Florida Gov. Jeb Bush and his wife Columba, and the late president's other living children - Neil, Marvin and Doro - lined the inner circle of mourners.
See photos from Bush's last journey to D.C. below.
A person familiar with the arrangements said the Bush team and Trump White House have been in close contact in planning an eventual funeral for the elder President Bush for months, marking a departure from what has been a long-running feud between President Trump and the Bush family.
An invitation-only funeral service will follow at Washington National Cathedral before his casket returns to Houston for burial.
The queen released a statement honoring Bush over the weekend, calling the 41st president "a patriot, serving his country with honor and distinction in office and during the Second World War".
Houston Mayor Sylvester Turner urged residents to wear colorful socks at an evening event in front of City Hall in a nod to one of the late former president's favorite fashion accessories. The commemorations conclude on Thursday, when the casket will be flown back to Houston for a service at St. Martin's Episcopal Church and buried at his presidential library in College Station.
Bush was elected USA president in 1988 as the successor to Ronald Reagan.