Three days after being appointed by Mattarella as prime minister, Giuseppe Conte, 53, has still not been able to form a government.
Writing on Facebook late on Friday, League chief Matteo Salvini, who insists on naming the noted eurosceptic Paolo Savona, 81, as economy minister, was blunt.
"I am really very angry," he raged.
The far-right leader doubled down on Saturday, tweeting images of cartoons in German media lampooning Italy, writing: "The newspapers and German politicians insult us: Italian beggars, idlers, tax evaders, freeloaders and ungrateful. And we should choose an economy minister that suits them? No thanks!"
Salvini reiterated his position later on Saturday after a meeting with party leaders, saying "the League has already taken enough backwards steps".
He added that he would give Conte the list of ministers the League wants on Saturday night.
Salvini had nominated Conte for the premiership with the support of Five Star leader Luigi Di Maio, but officially it is the head of state and the premier alone who appoint ministers.
And according to the Italian press, Mattarella will not bend for two reasons: to avoid isolating Italy in Europe and to protect the role of the president.
Conte met the president late on Friday to report "informally" on the discussions, but without presenting his final list of ministers.
Far from convinced of Conte's authority over the political heavyweights who will compose his team, Mattarella -- elected by a parliament which at the time was dominated by the centre-left -- wants Italy to respect its European
But Salvini, 45, emboldened by the March 4 election, does not intend to give up either, reportedly to the point that he is willing to "blow everything up" and return to the voters.
As guarantor of international treaties, Mattarella has been more discrete since the standoff began on Thursday. But he was clear in denouncing the "unacceptability of diktats towards the prime minister and president" by political parties.
The centre-left Democratic Party of former premier Matteo Renzi, however, did not pull its punches.
"You are playing around at the expense of the country just to defend your miserable interests," party leader Maurizio Martina said in remarks addressed to Salvini on Saturday.
There was no meeting scheduled for Saturday between Conte and the leaders of the League and Five Star, nor was there any indication that a solution could be found over the weekend.
Conte did however receive the support of French President Emmanuel Macron during a phone call on Saturday.
Macron gave the new Italian premier his best wishes for forming a government and said he would like to meet soon, Conte said on Facebook.
The impasse has already started to make financial markets nervous, with the Milan Stock Exchange closing down 1.54 percent on Friday. The difference in yield on Italian 10-year sovereign bonds compared to Germany's reached 217 points Friday afternoon -- the highest level since December 2013 -- before dropping slightly to 206 points at close.
Friday appeared to start positively, with Conte writing on his new Facebook page that his meeting with Di Maio and Salvini was "very profitable".
"The ministers I will be proposing will be politicians," he said.
But the exercise proved more complicated than expected for the little-known lawyer chosen by Five Star and the League because neither agreed to give the other the prime minister position.