Ronald Reagan arrived here too late for a peace demonstration aimed at him, but just in time for a lecture from Pope John Paul II about the importance of being a peacemaker.

In the Vatican Library, the president called his first European trip "a pilgrimage of peace." Obviously, he still has some distance to go in convincing the Italian left that he is born-again. And the pope--judging from the austerity, and even asperity, of his remarks--thinks that Reagan must try harder.

The peace march took place on last Saturday's sticky afternoon, and after meandering over much of Rome, halted at the beautiful round square called the Piazza del Popolo.

The attendance figures were still being debated as Air Force One set down the Reagans at Ciampino Airport. U.S. Ambassador Maxwell Rabb originally, and somewhat wistfully, put it at 20,000, a figure he revised upward today. The Italian state radio said 200,000; the Rome Daily American used 250,000.

Demonstrations are the haunt of this expedition. The ambassadors of the countries still to be visited by Reagan are constantly being consulted by the traveling party for estimates of turnouts. The staff broods on the melancholy prospect that the president could arrive home to the biggest, most embarrassing body count of all--at the special U.N. disarmament session in New York this weekend.

The Italian government was relieved by the Roman "manifestation." It was half the size of last October's nuclear protest. Italy is the only NATO country to choose a site for new U.S. cruise missiles, and a million signatures have been gathered on a petition to halt construction of the base at Comoso, situated in a remote corner of Sicily.

But the Italian peace movement ground almost to a halt last December when martial law was declared in Poland. Now, Italians are more concerned about the war that is--in the Falklands--than about wars that might be.

The communists appeared to have exclusive custody of the anti-nuclear issue. The red flags came thick and fast down the Via del Babuino, which empties into the piazza. The other political parties boycotted the march beause they thought it was unfair to target the American president alone.

The sponsors were somewhat self-conscious that the affair was colored so red. At the speakers' platform, set up outside Santa Maria del Popolo, the lovely Augustinian church where Martin Luther spent his last night as a Catholic, no communist banners were on view. Instead, the rainbow colors of the Committee of October 24, an ecumenical coalition, were displayed for world television.

Reagan took a pounding in the rhetoric painted on the sheets Europeans use for posters: "Reagan Brings War to Italy," "Reagan Executioner." He was hung in effigy from a Sicilian banner pole. Only two caricatures of the hundreds carried through the narrow streets depicted Soviet President Leonid Brezhnev as having anything to do with the arms race.

A young electrical engineer who walked behind a sheet proclaiming "Christians for Peace" identified himself as a Catholic and explained: "You see, it's Reagan who visits Rome, so we must address him." He said sadly that Catholics are not in the peace movement "because they are against the communists even more than the bombs."

Despite a great deal of hoarse chanting and upraised fists, the affair had a casual, picturesque Italian flavor. One grim-looking woman led her fluffy dog on a leash over the entire route. A man carrying the communist colors mopped his brow with the corner of his banner. During a pause in the passionate pleas for peace, the loudspeaker blared forth the martial strains of "The Ride of the Valkyries."

Talking to people in the crowd, it was strange to find how vague an idea they had of Reagan, the villain of the day. They like to think well of American presidents, but Reagan has not come through to them, except in his nuclear chit-chat.

"The men around him do not seem to be wise," said one woman peace marcher tactfully. Another said flatly, "He thinks seldom of world peace."

Apparently, the pope's views are something of the same.

Reagan was effusive in his praise of the pontiff, calling him "a holy man." The president spoke of the Constitution and the Ten Commandments. He justified U.S. foreign policy.

The pope did not return the compliments. Speaking slowly, he said that "humanity must be free, not only from wars, but from the fear that is generated by ever more sophisticated and deadly weapons."

The new peace pilgrim and the First Lady came out of the library into the baroque interior of the Clementine audience room. They were met with cheers and songs from U.S. priests and seminarians. The pope, who looked fragile and radiant, watched the enthusiasm, but eyed Reagan as if he were a new pupil who might not make the grade.