President Javier Milei brought Argentine biscuits with him to an audience with Pope Francis, as he sought to build bridges with a compatriot that he has severely criticised in the past.
The two men held talks for more than an hour before Mr Milei met the pope's top aides, with discussions including the economic crisis in Argentina, the Vatican said.
While campaigning for election last year, President Milei had sharply criticised the pope, accusing him of political interference and calling him an "imbecile" who "promotes communism".
But in an interview this weekend he described Francis, a former archbishop of Buenos Aires, as "the most important Argentine in history".
A video of today's meeting released by the Vatican showed the two men smiling and joking, and the president gave the pope gifts including Argentine biscuits that he is said to enjoy, officials said.
The president also hugged Francis when they met briefly at St Peter's Basilica yesterday, on the occasion of a papal mass for Argentina's first female saint.
The pope had brushed off Mr Milei's earlier criticism as rhetoric in the heat of a campaign, and called the newly-elected leader in November to congratulate him on his win.
The president asked Pope Francis to visit Argentina, a trip the 87-year-old has said he would like to make.
But no date has yet been set for the visit, which would be his first since becoming head of the Catholic Church in 2013.
Mr Milei also held talks today with Italy's President Sergio Mattarella and with Prime Minister Giorgia Meloni.
The president and Pope Francis were both born in Buenos Aires but have different views of the world.
One is a liberal economist and climate change sceptic on a drive to deregulate Argentina's economy.
The other is a champion of the poor who regularly attacks the power of financial markets and blames humankind for global warming.
After their talks, Mr Milei met Vatican Secretary of State Pietro Parolin and de facto foreign minister Paul Richard Gallagher.
Among the topics of discussion, the president and the pope "addressed the new government's programme to counter the economic crisis," the Vatican said in a statement.
Some 40% of Argentines are living in poverty, while crippling inflation tops 200%.
Elected on a wave of anger over decades of economic crisis, Mr Milei has embarked on major economic deregulation by presidential order.
He has devalued the peso, cut state subsidies and scrapped hundreds of rules.
His reform package hit a stumbling block last week, however, when parliament sent it back to committee for a rewrite, prompting Mr Milei to criticise his opponents, calling them "criminals" and "traitors".
In January, the president sent the pope a letter, saying a visit would "result in peacemaking and brotherhood for all Argentines, eager to overcome divisions and confrontations".
Throughout his papacy, Francis has railed against the inequalities generated by free markets, calling for the protection of society's most vulnerable.
During yesterday's mass, at which the 18th-century missionary Mama Antula was canonised, he again made a plea on behalf of society's most marginalised.
"How many suffering men and women do we meet on the sidewalks of our cities," Pope Francis lamented during his address.
Mama Antula, a consecrated Jesuit laywoman born Maria Antonia de Paz y Figueroa, is considered a champion of human rights from the period when Argentina was a Spanish colony.
President Milei had arrived in Rome from an official visit to Israel, where he made waves by likening Hamas's attacks on Israel to the Holocaust and announced plans to move the Argentinian embassy to Jerusalem.
Although from a Catholic family, he has expressed his fascination with Judaism and has been studying the Torah.
