BUENOS AIRES, Argentina — Argentina’s firebrand populist presidential candidate, Javier Milei, who is the front-runner to win the election later this month, is coming under fire from his rivals who blame him for a sharp fall in the local currency in the parallel market.

Mr. Milei has continued to tout his plan for dollarization of the South American country’s economy. With a little less than two weeks to go before the October 22 presidential election, the Argentine peso has sharply dropped over the past week.

The so-called blue rate, as the informal exchange rate is known, closed at around 1,025 pesos to the U.S. dollar on Tuesday, a sharp increase from 880 pesos on Friday. The rate was at 605 pesos a dollar before the upstart Mr. Milei rocked Argentina’s political landscape by unexpectedly emerging as the top vote-getter in the country’s national primaries on August 13.

Stringent capital controls mean that access to the official foreign exchange market, which currently prices a dollar at 367 pesos, is extremely limited, so parallel rates have flourished.

An anti-establishment candidate who admires President Trump, Mr. Milei has said he wants to replace the peso with the dollar and says Argentina’s Central Bank should be abolished.

The peso had already been steadily depreciating for months, but took a sharp downturn Monday after Mr. Milei, in a radio interview, recommended that Argentines not renew fixed rate deposits, saying the “peso is the currency issued by the Argentine politician, and therefore it is not worth crap.”

In recent days, Mr. Milei has suggested that the sharp depreciation of the peso could be convenient for his eventual presidency, saying that “the higher the price of the dollar, the easier it is to dollarize.”

The candidate for Buenos Aires mayor of Mr. Milei’s self-described libertarian party also called on citizens to drop the peso.

“Today more than ever: Don’t save in pesos,” Ramiro Marra wrote on social media Tuesday.

Mr. Milei’s opponents in the presidential race sharply criticized his words, saying he’s fomenting a run on the peso.

The presidential candidate for the governing Union for the Homeland coalition, Economy Minister Sergio Massa, said that some candidates are “capable of setting fire to a house for a vote.”

The candidate of the main opposition coalition called United for Change, Patricia Bullrich, said Tuesday that “between Massa, the arsonist who is leading us into hyperinflation, and Milei’s irresponsibility, which encourages the currency run, there are Argentines distressed about the present and the future.”

The depreciation of the peso will accelerate the already red-hot inflation that was at an annual rate of 124 percent in August.

Banking associations published a news release calling on candidates to “show responsibility in their campaigns and public statements.” Without ever naming Mr. Milei, the associations wrote that “recommending not to renew deposits doesn’t do anything other than generate concern in a sector of the population.”

Mr. Milei, who has received support by characterizing himself as a political outsider who will battle the “political caste,” pushed back against the criticism, saying there are some who are “trying to gain political advantage from the economic collapse by inventing responsibilities.”

“If you want to find those responsible, look in the mirror,” Mr. Milei, wrote on social media.