Though weak and frail, the pope stood up from his chair as the president entered the papal offices, reports CBS News White House Correspondent Mark Knoller.
Afterwards, White House spokesman Ari Fleischer said Mr. Bush did raise his concerns about "the standing of the Catholic church" in America, but Fleischer would not elaborate.
As Mr. Bush said goodbye to John Paul, the pope was heard to say "God bless America."
The president, in Italy for a meeting of NATO and Russian leaders at an airbase outside Rome, met the pope at the end of a week-long European trip. He arrived amid tight security in a long motorcade of U.S. and Italian cars with all traffic around the Vatican blocked.
Upon arriving at the papal palace, the president was escorted past a row of Swiss Guards in red-plumed helmets and into a study where the pope stood waiting beside his desk.
At a NATO-Russian summit before the meeting, Mr. Bush described the pope as "a man of enormous dignity and compassion," and expressed a desire to discuss alleged sexual improprieties committed by priests in the United States.
"I say that because the Catholic Church is an incredibly important institution in our country," President Bush said. "I'm also going to mention the fact that I appreciate the Pope's leadership."
Last month, the pope summoned U.S. cardinals to the Vatican to discuss the sex scandals. He condemned sexual abuse by priests as criminal, and said there is no room in the priesthood for those who engage in such behavior.
Mr. Bush's comments were his first on the matter since March, when he said he was confident the church would "clean up its business."
He backed embattled Cardinal Bernard Law of Boston, who has become a lightening rod for criticism since. "I respect him a lot," Mr. Bush said in March shortly after Law had given prosecutors the names of at least 80 priests accused of sexually abusing children.
Roman Catholic voters are highly sought after, because they tend to switch party allegiances from election to election according to the candidate they prefer, and often can tip the balance at the ballot box.
Polls show Americans are disappointed by the church's handling of the sex abuse situation.
The child sex scandal, which began in the Boston archdiocese, shows little sign of abating.
Last week Milwaukee's now-retired archbishop Rembert Weakland admitted he paid off a former theology student to keep quiet about an alleged sexual encounter two decades ago.
In Boston, court documents released in the sex abuse case of defrocked priest John Geoghan showed Cardinal Bernard Law knew of allegations against Geoghan but failed to keep him away from children.
The scandal has spread across the country, involving many dioceses. Priests have been suspended or forced to step down over allegations and some have been charged criminally.
New York's archbishop, Cardinal Edward Egan, has been under fire for alleged laxity in disciplining pedophile priests and assisting victims, both in New York and previously as bishop of Bridgeport, Connecticut.
In Los Angeles, Cardinal Roger Mahony, head of the largest American archdiocese, has admitted keeping secret a case of child sexual abuse by a priest for 14 years, and apologized for his inaction.
A suit in that case was filed in federal court last week.
U.S. bishops gather next month in Dallas to formulate a policy on how to deal with priests accused of sexual abuse.
Relations between President Bush, a born-again Christian, and the pope have been generally good, a marked contrast with the Vatican's relations with President Clinton.
Relations with the Clinton administration were marred by a bitter clash between the U.S. and Vatican delegations over abortion rights at a 1994 U.N. population conference in Cairo.
Like his father, Mr. Bush and the pope see eye-to-eye on major issues of morality, sharing the same tough anti-abortion stance.