US President Barack Obama spoke of his admiration for Pope Francis and invited him to the United States at their first talks, but got a reprimand for contraception clauses in his healthcare reform act.
Obama said he had been "extremely moved" by the Catholic leader's message of compassion for the needy and said their conversation had focused on the need to address "growing inequality" and to show "empathy".
"His Holiness has the capacity to open people's eyes," Obama said at a joint press conference with Prime Minister Matteo Renzi after his Vatican visit.
The president also spoke of the "opportunity" for immigration reform in the US after Francis stressed the plight of families that are being divided by deportations and are forced to "live in the shadows".
The Vatican said in a terse statement that the two sides had discussed "the exercise of the rights to religious freedom, life and conscientious objection" - a reference to Obama's Affordable Care Act (ACA).
It said these issues were "of particular relevance for the Church" in the United States, following a Supreme Court challenge against the law by Christian employers which is expected to lead to a ruling in June.
The issue of "Obamacare" and its clause forcing private employers to provide health coverage for contraception for their employees has incensed US Catholic leaders who say that it infringes on religious freedoms.
"I pledged to continue to dialogue with the US Conference of Bishops," Obama said, referring to a conversation with the Vatican's Secretary of State Pietro Parolin after his meeting with Pope Francis.
Obama said there was a need to "strike the right balance" between providing healthcare for women and ensuring "that religious freedom is still observed".
"I explained to (Parolin) that most religious organisations are entirely exempt," said Obama, who has also faced criticism from Catholic leaders for his support for gay marriage and abortion rights.
Controversy over "Obamacare" and the president's drop in popularity could help Republicans in this year's mid-term congressional elections, which would weaken the US leader for his remaining two years in power.
Obama told Francis he was a "great admirer" at the start of their talks at the Vatican, which political observers said could have been a bid to boost the US president's support at home among Catholic voters.
"I invited and urged him to come and visit the United States," Obama said after Catholic groups spoke of a possible papal visit for the Church's World Meeting of Families in Philadelphia in September 2015.
The closed-door talks between the first African-American US president and the first pope from Latin America lasted around 50 minutes - slightly longer than papal meetings with other world leaders.
The two exchanged gifts afterwards, with the Pope offering Obama a copy of his "apostolic exhortation" from last year in which he excoriated global capitalism with an invective against the "cult of money".
"I actually will probably read this in the Oval Office when I'm deeply frustrated. I'm sure it will give me strength and calm me down," a smiling Obama said.
