Mr Renzi, 41, promised the president he would wait until the Senate voted through the government`s 2017 budget before handing in his resignation.
The Senate was holding a vote of confidence on the budget on Wednesday.
Italians voted by a margin of 59% to 41% against Mr Renzi`s plans for constitutional reform, prompting his decision to stand down.
He is thought to favour early elections or a wider "government of national responsibility" involving other political parties. Mr Renzi was expected to put the idea to both the PD and President Sergio Mattarella.
It is also unclear who would lead and take part in such a caretaker government. PD Finance Minister Pier Carlo Padoan`s name has been suggested, along with Senate leader Pietro Grasso, who is apolitical.
However, it is up to the president to decide what happens next. Mr Mattarella is widely known to be against early elections, and according to a source quoted in Italy, believes it is "inconceivable" that elections can be held before the electoral laws governing both houses of parliament are synchronised.
The law was changed to an "Italicum" system last year to give the leading party a parliamentary majority through bonus seats in the lower Chamber of Deputies. But there has been no such change in the Senate, which is elected by proportional representation.
Senate reforms were part of the package rejected on Sunday. Another factor is that the constitutional court will rule on 24 January on whether the lower house reforms are legitimate.
Italy`s political turmoil has also led to days of uncertainty in international markets, amid questions over the fate of Italy`s indebted banks, especially its third largest, Monte dei Paschi, which is seeking €5bn (£4.2bn; $5.3bn) to recapitalise.
The markets moved higher and Italy`s government bond yields fell on Wednesday amid reports that the government in Rome was preparing to take a €2bn controlling stake in the bank and to ask for a €15bn eurozone loan to bail out the troubled banks.
Two of the big winners in Sunday`s referendum were the anti-EU Northern League and anti-establishment Five Star Movement, and both parties are pushing for early elections.
But other parties, such as the centre-right Forza Italia, are trailing in the polls and want elections delayed. Forza Italia leader Silvio Berlusconi, 80, had tests in a Milan hospital on Wednesday, six months after he had heart surgery.
Mr Renzi`s government still has 14 months of its mandate remaining.
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