President Sergio Mattarella meanwhile was working through the Feast of the Immaculate Conception public holiday, preparing for 48 hours of consultations aimed at brokering a deal on what follows the resignation of Italy's youngest premier after two years and 289 days in office.
By Saturday, the former constitutional court judge will know if there is the basis for a stable cross-party coalition government that can guide Italy to the end of the current parliament in February 2018.
If there isn't, the head of state will have no choice but to call early elections with a ballot feasibly taking place as soon as February.
That would be just after the constitutional court is due to deliver its verdict on a new electoral law for the Chamber of Deputies that was adopted earlier this year.
But it would not allow enough time for any revision of the law before the election, or for changes to the different set of rules that applies to the Senate.
Analysts see this issue as making an election later next year after a period of caretaker rule as the most likely outcome.
Mattarella accepted Renzi's resignation on Wednesday evening, three days after the 41-year-old suffered a chastening defeat in a referendum on constitutional changes he had championed.
Knives being sharpened
The outcome left the centre-left leader with little option but to quit.
But he retains the leadership of his Democratic Party, the biggest force on Italy's centre-left. And he indicated as he resigned that he intends to pursue his political career and a reformist agenda that won plaudits from the likes of US President Barack Obama and German Chancellor Angel Merkel.
Renzi received a boost on Thursday with a poll published by La Stampa daily, conducted a day after the referendum, giving the PD the backing of 32.5 percent of voters, ahead of the populist Five Star movement with 27 percent.
And 57 percent of centre-left voters saw Renzi as the best leader available to the PD.
But there were also signs of knives being sharpened within the party after the referendum vote which Renzi's critics see as having eroded the party's base among the working class and young voters hardest hit by Italy's economic problems.
"Today is not the moment for rows but there are many things to be discussed and analysed. We have to understand the message the referendum sent us," said Roberto Speranza, one of a number of PD lawmakers who voted against Renzi in the referendum.
Luigi Zanda, head of the PD group in the Senate, acknowledged that "there are tensions within the party" but said he expected the need for unity to prevail.
Renzi admitted to the party's executive that he anticipated a "tough debate" over the lessons of the referendum and said he was open to proposals being aired of trying to create a broader coalition of the Italian left.
Debt outlook downgrade
But that idea was shot down by veteran leftist Nichi Vendola.
The former governor of the southern region of Puglia said Renzi had burnt his bridges with progressive forces.
"If reformism means having a left elite do the work of the right the result is inevitably catastrophic," Vendola told La Repubblica.
Before handing back the keys to his Palazzo Chigi residence, Renzi insisted the PD was ready for an early election battle with the ascendant Five Star Movement, the far-right Northern League and Silvio Berlusconi's fading Forza Italia.
"We are not afraid of anything or anybody," Renzi said.
Five Star and the Northern League are both demanding an early election. Italy's entry into a period of political uncertainty has not created the kind of market turmoil some had predicted and a feared crisis in the banking sector has not materialized as a rescue plan for the most troubled lenders has begun to take shape.
Moody's ratings agency has however downgraded its outlook for the country's sovereign debt to negative from stable, saying the failure of the constitutional referendum slowed reform progress and left Italy more exposed to "unforeseen shocks".
By Angus MacKinnon