He led his Western-backed March 14 alliance to victory in parliamentary elections on June 7, winning 71 seats to keep control of the legislature from a rival bloc including Hezbollah, a political group backed by Iran and Syria, which enjoys strong support among Shia Muslims.
"We hope to have a harmonious government that will respresent the interests of all Lebanese people," Hariri said after meeting Sleiman.
He pledged to protect the interest of all Lebanese, including those who voted for the opposition alliance.
Hariri, a Sunni, had courted support from both sides of Lebanon's political divide in recent days, supporting Nabih Berri, the leader of Amal, another party with a Shia Muslim base, for re-election as speaker and meeting Hassan Nasrallah, the Hezbollah leader.
However, only 15 of the opposition alliance's 57 MPs backed Hariri when asked by Sleiman.
Members of this bloc are likely to be asked to join a national unity government, but Hezbollah has previously demanded a minority veto, which Hariri has repeatedly refused.
"We will begin consultations with all parliamentary blocs," Hariri said on Saturday.
Abbas Hashem, an MP from the Change and Reform opposition bloc of Michel Aoun, told Al Jazeera that they would not join the government if they "did not have the power to make decisions".
"We are not going to be in partnership without a certain kind of power," he said. "I am sure that Saad Hariri will be will be able to provide the opposition with the opportunity ... at least to be a partner in unity."
But Mohammed Qabbani, an MP from Hariri's Future bloc, told Al Jazeera that the new prime minister-designate would not accept any call for an opposition veto in the cabinet.
"What the new prime minister wants is a national unity government, but he also wants to stick to the constitution and will not accept conditions like vetos," he said.
"We have tried this formula in the present government and it was paralysed."
Rami Khouri, director of the Issam Fares Institute for Public Policy and International Affairs in Beirut, told al Jazeera that there was now likely to be a lot of bargaining while the rival political blocs resolve two major issues.
"One is the apportionment of seats in the cabinet between the various groups in the country, the government majority, the opposition minority and the independent group that would be headed by the president," he said.
"The challenges that face Lebanon are real and huge, but the chances that have been given to us are bigger than that"
"The other is the substantive issues that they have to agree on in the cabinet - internal issues, regional issues, international issues, political economic and military issues."
Khouri said that for the first time in many years Lebanon appeared to have a functioning political system that everyone seemed interested in seeing succeed.
"You have a legitimate prime minister with a majority that was elected ... you have a president that has credibility, support and is widely respected, and you have an opposition that is prepared to play the democratic game," he said.
Speaking on Saturday, Hariri said that Lebanon faced sizeable challenges in bringing togther the country's various groups and addressing the economic situation.
"The challenges that face Lebanon are real and huge, but the chances that have been given to us are bigger than that," he said.
Tensions between supporters of the two blocs threatened to boil over into a civil war last year as Hezbollah fighters and their allies routed their rivals in Beirut and the mountains to the east.
A Qatari-sponsored deal in May 2008 defused the crisis, but sectarian tensions rose again in the run-up to the election.
Hariri has twice passed on the chance of becoming prime minister, preferring to giving the post to his father's senior aide, Fouad Siniora, to avoid some of the political tension and direct challenge that Hezbollah posed at the time.
Hariri was raised in Saudi Arabia and is seen by some in Lebanon as a symbol of Riyadh's influence in the region, which is rivalled by Damascus.
"The designation of Hariri is not separate from the continued deliberations between Syria and Saudi Arabia over the future political power-sharing in Lebanon," Lamis Andoni, Al Jazeera's Middle East analyst, said.
"It is clear that Saudi Arabia has secured implicit Syrian support for Hariri's designation.
"This is an important message to Hezbollah and its allies who have to rely more on their local power than on the support of Damascus and Tehran."