Under the current system, the Culture Ministry manages Italy’s museums and directors have little autonomy. The changes are intended to help bring museums closer in line with counterparts like the Louvre and the Prado. They also seek to give directors more influence over budgets and ease the way for them to raise private funds to help offset drastic cuts in state funding.

The goal is also to allow directors to make Italy’s art-rich but often fusty museums easier for tourists to navigate — with better presentation, labels and organization.

“It’s a giant leap ahead,” Dario Franceschini, Italy’s culture minister, said in a recent interview in his ballroom-size office. “Italian museums should be more dynamic. They should have more bookshops, more restaurants. They should be attractive and have more multimedia.”

Mr. Franceschini has championed the changes at the Culture Ministry as part of the can-do spirit of the government of Prime Minister Matteo Renzi, who faces the challenging task of rousing Italy from a protracted recession.

But the changes have also raised concerns that the new hiring criteria will favor marketing savvy over conservation and risk putting too much power in the hands of revolving-door culture ministers rather than longtime state culture officials. Others said the changes did not provide museums with enough autonomy, given that museum employees will remain part of the Culture Ministry bureaucracy.

Simply changing directors won’t have any effect “if the state doesn’t change, if the structures of the museum don’t change,” said Antonio Natali, director of the Uffizi. He also said that unless the director has control of the museum’s crucial technical, administrative, legal and personnel offices, then “not even the descent of a new redeemer” would make Italian museums function at their best. Last year, the country’s museums attracted more than 40 million visitors and took in nearly 135 million euros, or $156 million, the Culture Ministry said. By making the most-visited and highest-earning museums more independent, the ministry hopes they will generate more revenue. Under the current system, the proceeds from ticket sales go directly to the state and directors have little incentive to draw more visitors, raise private funds or set up profit-generating cafeterias and shops.

Beyond the 20 top museums, the changes would reorganize thousands of other Italian museums into regional clusters and offer a combined ticket, encouraging tourists to visit multiple museums. “A country with 4,000 museums should see this as a formidable economic resource,” Mr. Franceschini said. “Italy’s challenge is to offer quality tourism,” he added.

The 20 top museums include some of the most-visited in Italy — the Uffizi, the Pinacoteca di Brera in Milan, the Archaeological Museum in Naples — but also sites that the ministry thinks have untapped potential, like the archaeological museums in Taranto and Reggio Calabria in southern Italy.

The new directors are expected to be in place by the summer and will serve four-year terms before the positions reopen. The current museum directors — typically experts in art history, archaeology or architecture but for the most part with little professional training in arts management — will have to reapply for their own jobs. Mr. Natali of the Uffizi said he would do so “to keep faith in my dignity as a man.” Since the job was posted on Jan. 8, at least 50 people have applied. The Italian-language application has been downloaded 12,000 times and the English application 50 times, a spokesman for the Culture Ministry said.

Mr. Franceschini said he hoped the search would attract international applicants. But while salaries for the new directors — from 78,000 euros ($91,000) to 145,000 euros ($170,000) — are high for Italy and competitive in Europe, they pale in comparison to those of their counterparts in the United States, where the director of the Metropolitan Museum of Art in New York earns more than $1 million a year.

Most Italian cultural experts welcomed the changes, with some reservations. “It opens the possibility for a new era of management of Italian museums,” said Stefano Baia Curioni, a professor of cultural policy at Bocconi University in Milan. “But the crucial point is that the minister has to nominate a committee that’s outside of the game, that can make selection in an independent way.”

Under the present system, museum directors are named by career state culture officials, not by the minister, who is a political appointee. After the Feb. 15 deadline, a five-member committee selected by Mr. Franceschini will choose a shortlist of three candidates for each museum, and he will make the final decisions this spring. Mr. Franceschini dismissed the idea that the changes would centralize power and run the risk of cronyism. “The selection procedure presupposes that very high-level candidates will apply,” he said, adding that committee members will also be able to give their recommendations.

Some worry that the changes might be the first step toward dismantling an established and widely respected system of cultural stewardship and replacing it with one that favors crowd-pleasing blockbuster shows over quality and research.

“One word of caution is that museums have to educate and not entertain, that’s the bottom line,” said Daniel Berger, a longtime adviser to the Culture Ministry. “They are the font of Italy’s cultural heritage and collective memory.”

Many experts acknowledge that the ministry’s mandate is primarily conservation, rather than making museums appealing to visitors.

“There is social, cultural, educational value in museums that is underused because of the current system of cultural management,” said James Bradburne, the director general of the Palazzo Strozzi in Florence. “If, on the other hand, it is just a way to get politicians closer to the decision-making structure to transform them into tourist cash cows,” he added, “then it’s a mistake.”