At the very outset, he thanked his defeated rival, former Vice-President Al Gore, for a "contest conducted with spirit, and ended with grace".
"You may not have voted for me, but I intend to serve as your President."
November's disputed election provided the subtext for the speech.
At the very outset, he thanked his defeated rival, former Vice-President Al Gore, for a "contest conducted with spirit, and ended with grace".
Large portions of the rest of the speech seemed to be targeted at Americans who had voted for Mr Gore.
A line included very high up in the speech - "while many of our citizens prosper, others doubt the promise - even the justice - of our own country" - would have reverberated in some Florida counties, where many African-Americans think they were unfairly denied the vote.
More like a sermon
"Sometimes our differences run so deep, it seems we share a continent, but not a country," said the new President.
The speech was solemn and short on applause lines - in this sense it read more like a sermon than a political speech.
On numerous occasions, he invoked the name of God. Mr Bush is a deeply religious man, and his faith found expression in the address.
Yet he took the chance to advance his legislative agenda, calling for reforms in education, social security and tax cuts to give fresh impetus to the economy.
But it was thematic, rather than specific - and ended on a call for reaffirmation of citizenship.
"I ask you to be citizens," he said. "Citizens, not spectators. Citizens, not subjects. Responsible citizens, building communities of service and a nation of character."
A new chapter
As ever in inaugural addresses, there was a strong sense, too, of national renewal - that America's extraordinary democratic experiment was being refreshed and enhanced.
"This work continues. The story goes on. And an angel still rides in the whirlwind and directs this storm," he said.
It was certainly the most elegant and eloquent speech of Mr Bush's career, and his delivery was assured.
He lacks the rich baritone voice and presentational craft of Ronald Reagan, and the folksy charm and warmth of Bill Clinton. But his speaking style is honest, uncomplicated and direct.
This was a heartfelt speech - his call for national unity genuine. He hopes it will set the tone for his four years in office.