The honeymoon seems to be over for Pope Francis.

New figures published by the Vatican show that the 79-year-old Argentine Jorge Mario Bergoglio, who won election to the papacy in 2013 and rode a groundswell of public support for what were seen as relatively modern views, is drawing smaller crowds and possibly alienating the base of traditional Catholics.

In 2015, more than 3.2 million pilgrims visited and attended papal events, liturgies or prayer services at the Holy See, the Vatican said at the end of December. That was a sharp drop from the 5.9 million visitors received by Pope Francis in 2014. And it was less than half of the 6.6 million pilgrims who visited the Vatican during the first nine-and-a-half months of his pontificate in 2013.

The Vatican attributed the fall, in part, to terrorism fears keeping people from visiting Rome.

But pope-watchers say there's another factor at work: his comparatively liberal views on some hot-button social issues, including gay rights, and whether Catholics who have divorced and civilly remarried should be allowed to receive communion. Those views, which have won Pope Francis positive coverage in the media, may be turning off devout Catholics.

The decline is a surprising trend for a pope who has appeared to reinvigorate the Catholic Church with his humble ways, his focus on the poor and his fight against corruption. Francis gained new admirers even among the not-so-faithful, earning the nickname "The People's Pontiff.”

His popularity is higher outside the Catholic world than inside — Sandro Magister

"His popularity is higher outside the Catholic world than inside,” said Sandro Magister, a Vatican expert and author of several books on the Roman Catholic Church.

Magister dismissed the Vatican's terror-threat argument — noting that attendance figures to the Pope's weekly general audiences in Rome were higher last December (44,000), after the Paris attacks, than the year before (32,000) — and said the Church's “more modern approach" to crucial issues such as gay rights is a more important factor.

A few months after his election, Francis reaffirmed the Roman Catholic Church's position that homosexual acts were sinful, but being gay was not. The statements were hailed as a historic softening of the Vatican's position on the issue, although there has been much debate over the meaning of the Pope's words.

“His popularity has been pushed by high expectations in the initial part of his papacy,” Magister said, but they “they have not been followed by pragmatic gestures.”

Homosexuality remains a taboo within the Vatican, as and the question of offering communion to divorced believers remains undecided.

The Vatican suggested a different interpretation of the new data. “We got back to more normal figures” after the "novelty effect" at the start of Bergoglio's tenure, said Father Federico Lombardi, the Vatican spokesman, speaking to Italian news agency Ansa.

The latest numbers are almost in line with those of Francis' predecessor, German Joseph Ratzinger, whose public attendance figures peaked in the first full year of his papacy in 2006 at 3.2 million.

Lombardi insisted that the Pope does not gauge his papacy “on the number of participants” in Vatican events.

But it's clear that the Pope is proving divisive among hard-core Catholics, who remain suspicious of a pontiff who plays to the general public, said John L. Allen, author of nine books on the Vatican and Catholic affairs.

Francis is an activist Pope, with a clear ecclesiastical and political agenda — John L. Allen

“Ironically 'deep Catholics' generally have made their peace with the idea that the Church and the Pope will not be liked by the outside world, and when they see a popular Pope it makes them nervous,” Allen said. “Francis is an activist Pope, with a clear ecclesiastical and political agenda, and like any other leader who’s trying to shake things up, he’s to some extent divisive.”

The Pope has also not proved to be a magnet for people converting to Catholicism or attending Sunday mass, according to data.

In Italy, attendance at places of worship decreased in 2014 to 28.8 percent of the population compared to more than 30 percent during the years of Ratzinger, according to Istat, the Italian statistics bureau.

The Union of Rational Atheists and Agnostics in Italy reported last week that online applications to download a form allowing people to “de-baptize” themselves, meaning to formally request to be taken off the Church’s rolls as a member, reached an all-time high in 2015 of 47,726.

Something else unexpected occurred when Francis traveled to the U.S. last September. His visit had a positive impact on views on the Church, especially among Democrats and liberals, data from the Pew Research Center show.

But the study also showed that the Pope's traditional surge in popularity after a visit to a country did not materialize this time. Straight after his American tour, favorable views of the Francis reached 81 percent among Catholics and 68 percent in the general public. When Ratzinger visited in 2008 he scored higher among Catholics (83 percent) and lower in the general public (61 percent).

That's not to say the the American reaction was cold, Allen said. The Pew data “also found that Francis overall has an almost 70 percent favorability rating in the States, which, when you compare it to politicians — for instance, Obama — is terrific.”