Letta - who heads Italy's first grand coalition right-left cabinet since the Second World War - said he was apologizing "on behalf of a political class that for a very long time pretended not to understand that through its words, actions and omissions, it was letting passion, sacrifice and competence go to waste".
"The biggest debt that we are accumulating, by repeating the mistakes of the previous generations, is towards the young people, which is an unforgivable mistake," Letta wrote in a letter published in La Stampa newspaper.
The unemployment rate in the eurozone's third largest economy reached a new record of 12 percent in April, official data showed on Friday.
Youth unemployment, which will be a key focus for European leaders at a summit in Brussels later this month, rose to 40.5 percent with an estimated 656,000 Italians aged 15 to 24 looking for a job.
In an article on Sunday, La Stampa said 316,000 young Italians had emigrated over the past decade, with most seeking a brighter future in Germany, Britain, France and the United States.
Letta, who became premier in April after a general election led to a two-month political deadlock, said the fate of the country's youth was his government's top priority.
The moderate leftist vowed to push for action to make it easier for companies to hire youngsters, to support innovation and education and to "free up the energy of a country stifled by privileges, bureaucracy and conservatism".
The government "will do its utmost" to give young Italians the opportunity to choose freely whether they want to stay or leave "and eventually return to contribute to the difficult but not impossible rebuilding of the future," Letta said.