Michel Aoun convened a meeting with ministers and top security officials at Baabda palace, telling them that political leaders had been responsive to calls for calm, his office said.
"He stressed that security, economic, financial, and political stability is a red line," Justice Minister Salim Jreissati said after the meeting.
Aoun will take no steps to decide on whether to accept the resignation before Hariri returns from abroad, said Jreissati, who is politically aligned with Hezbollah.
"The president is waiting for Hariri's return to hear from him personally," he said. "This indicates a sovereign vision... and that the resignation must be voluntary in every sense."