Lebanon's President Michel Aoun on Wednesday asked Saad Hariri to stay on as caretaker prime minister the day after Mr Hariri tendered the resignation of his government.
Mr Hariri announced his intention to step down after 13 days of mass protests in Lebanon against corruption, ineffectual governance and financial collapse.
Mr Aoun said on Tuesday that he would speak with political parties before announcing his decision.
While he issued a short statement on Wednesday accepting Mr Hariri's resignation, he said he would address the nation on Thursday at 8pm local time.
But Mr Aoun told a delegation from the Maronite League on Wednesday that a new administration must be formed quickly or “people will return to the streets.”
He said that “Lebanon will have a clean government", one that is not tainted by corruption.
Lebanon's government now becomes a caretaker administration. It will rarely meet but ministers will stay on to oversee daily operations.
The president will consult with political parties to pick a new prime minister-designate.
One option being put forward by Mr Hariri's allies is for him to lead a technocratic administration to fix the financial crisis and meet the demands of protesters.
He would accept the nomination to become prime minister-designate in this case, sources close to him told Reuters.
The announcement by Mr Hariri on Tuesday was met with cheers on the streets, where tens of thousands have been gathering for the past two weeks demanding a change in governance.
It is unclear how quickly a new administration could be put together given the deep divisions between parties on how to fix the crisis.
Lebanon appeared to be returning to a semblance of normality on Wednesday, with the army opening roads and banks set to open again on Thursday.
Banks have been closed since the day after the start of the protests on October 17.
The Association of Banks announced on Wednesday that work would resume on Thursday, although branches would remain closed until Friday.
There have been concerns about liquidity after the long closures.
Fitch Ratings cut the long-term default rating of two of Lebanon’s largest lenders because of further liquidity risks after Mr Hariri's resignation.
Bank Audi and Byblos Bank were downgraded to CCC-minus from CCC, with both lenders also placed on a negative rating watch, Fitch said.
"In our view, deposit stability is now at greater risk as depositor confidence has also suffered,” it said.
Major universities that have been closed since the start of the protests will reopen on Thursday.
The American University of Beirut, the president of which has actively supported the demands of protesters, and the Lebanese American University will resume classes.
Exams missed will be rescheduled. Schools will also reopen, the Education Ministry said on Wednesday.
The UN this week called for Lebanese leaders to take decisive action and form a new government quickly.
Central Bank Governor Riad Salameh said on Monday that the country needed an economic plan in days or it risked a financial meltdown.
Finance Minister Ali Khalil on Wednesday announced an extension for businesses to submit tax records and payroll figures without incurring fines because the ministry has been closed.
Roadblocks have been a main tool for the protest movement to apply pressure to the government.
Fuel importers said this week that without banks reopening and roads clearing, petrol stations would begin to run dry in a few days.
There have also been concerns about shortages of other staples becasue of the road closures.