Argentina's stock market reacted with optimism Tuesday to the resounding election win by libertarian Javier Milei, despite the country being gripped by uncertainty over what changes the self-described "anarcho-capitalist" will bring.

Milei, a 53-year-old economist who has vowed to scrap multiple government departments and sometimes campaigned by waving a chainsaw from the stage, trounced Argentina's long-dominant Peronist coalition as voters punished the government for decades of economic decline.

Latin America's third-biggest economy is creaking under annual inflation of 143 percent.

Monday, the day after the election, was a public holiday in Argentina, delaying the market reaction.

But immediately Tuesday, the stock market opened up 20 percent and held its strong gains, eventually closing 17.7 percent higher.

On the same day, the president-elect also received a call from Pope Francis, who himself is Argentinian and had been the target of insulting comments from Milei, who during his campaign had accused the pontiff of "promoting communism." He later apologized.

In his congratulatory call to Milei the Pope expressed "wishes of union and progress for our country," the president-elect's office said, while Milei noted he invited Francis to visit Argentina.

Argentina's peso is strictly controlled, and the informal "blue dollar" exchange rate — seen as a barometer of panic in the country — reacted with moderation, rising slightly to 1,050 pesos to the dollar.

The rate is almost three times the official rate of 371.50, and analysts warn a devaluation is long overdue.

Milei has vowed to ditch the peso for the US dollar and shut down the central bank — which he accused of rampant money printing to finance government overspending — in a bid to halt inflation.

During his campaign, he said he would slash state spending and ditch about 10 government ministries, among other controversial proposals.

He later toned down some of his rhetoric, leaving uncertainty over his actual plans.

'Own goal'

While stocks reacted favorably to Milei's win, Mexican President Andres Manuel Lopez Obrador was less enthusiastic, comparing the election to his own goal in soccer.

"With all due respect, it was an own goal and I do not agree, although I respect the decision of the people with right-wing governments," he told a Tuesday news conference, without directly naming Milei.

Analysts have said that, given Argentina's massive problems, any fixes are going to inevitably bring economic pain.

In his first interviews on Monday after the election, Milei warned it would take up to two years to tame inflation, and laid out his plans to reform the state.

Milei said "everything that can be in the hands of the private sector is going to be in the hands of the private sector," including the state oil company YPF and state media.

The rise in Argentina's stock market was led by majority state-owned oil company YPF whose shares rose 36.5 percent after Milei's remarks.

On Monday, YPF shares listed on Wall Street were up 40 percent at closing, dipping a little more than one percent by close Tuesday.

Milei also said he would push for the elimination of strict currency exchange controls — with analysts saying the official rate of the peso to the dollar is an expensive fiction.

Asked about his dollarization platform, Milei said the priority was "to close the central bank. Then the currency will be the one that Argentines freely choose."

Milei on Monday held his first meeting with outgoing President Alberto Fernandez to coordinate what the incoming leader called an "orderly and responsible" transition ahead of his inauguration on 10 December.