The frail 82-year-old pontiff reaffirmed "his faith in the spiritual resources of American Catholics," a spokesman said, describing the leaders' private discussion yesterday.
In a brief session before news cameras, John Paul labored to stand to bid Bush farewell with a quiet "God bless America."
His parting words to the president: "I hope to be able to meet you again."
There have been reports that the ailing pope might consider resigning should his health worsen, although Vatican officials have denied that he has such plans.
Swiss Guards in red-plumed helmets stood at attention, with 15th-century halberds at their sides, as Bishop James Harvey, an American ordained in Milwaukee, escorted the president through Vatican corridors of marble.
"I will tell him that I am concerned about the Catholic Church in America, I'm concerned about its standing," Bush told reporters before the meeting. "I say that because the Catholic Church is an incredibly important institution in our country."
Bush has assiduously courted Catholic support - often meeting with local bishops when he travels outside Washington, inviting members of the church hierarchy to the White House - after splitting Catholic votes with Democrat Al Gore in the 2000 election.
Roman Catholic voters are highly sought after because they tend to switch party allegiances from election to election depending on the candidate, and they often can tip the balance at the ballot box.
Polls show Americans are disappointed by the church's handling of accusations of sexual abuse of children by priests.
Bush's comments were his first on the scandal since March, when he said he was confident the church would "clean up its business."
At that time, he backed embattled Cardinal Bernard Law of Boston, who has since become a lightning rod for criticism. "I respect him a lot," Bush said in March, shortly after Law gave prosecutors the names of at least 80 priests accused of sexually abusing children.
The president had no public comment after his meeting with John Paul, but White House press secretary Ari Fleischer confirmed that Bush delivered the message of concern as he said he would.
Vatican spokesman Joaquin Navarro-Valls said the pope, in turn, "wanted to express, despite the difficulty of the moment, his faith in the spiritual resources of American Catholics committed to bear witness to the values of the Gospel in society."
Bush, in Rome for a NATO-Russia meeting earlier in the day, described John Paul as "a man of enormous dignity and compassion."
In the noisy clatter of camera shutters that accompanied their greeting, John Paul jokingly raised his hands to cover his ears, and the president teased him: "They'll make you look good, your Holy Father."
The visit was Bush's last stop on a weeklong tour through Europe and Russia. He left for Washington late yesterday afternoon.