Sleiman, an ex-army chief, was elected in a parliamentary session after Sheikh Hamad bin Khalifa Al-Thani, the emir of Qatar, helped broker a deal to end a dispute between rival factons.
Zeina Khodr, Al Jazeera's correspondent in southern Beirut, said the early portion of Nasrallah's speech praised the resistance against Israel.
"He is giving credit to the resistance that actually led to the Israeli withdrawal from Southern Lebanon, even giving examples from Palestine and Iraq," he said.
But Khodr also said that he had sought to downplay suggestions that recent clashes in Beirut between pro- and anti-government forces were a sign of a growing sectarian divide in Lebanon.
"He said that in every country, there is disagreement - those who support resistance and those who do not," she said.
"He is trying to show that the battle and the power struggle in Beirut was not a Sunni-Shia clash - it was simply a power struggle between those who support the resistance and the other, who do not believe in the resistance's weapons," she said.
Appeal for reconciliation
Of those voting in Lebanon's 127-member parliament on Sunday, 118 voted in favour of Sleiman becoming president.
Six of the ballots cast were blank, signifying a protest vote or reservations over Sleiman's election.
In his inaugural speech on Sunday, Sleiman appealed to Lebanese political factions to work together to avoid internal strife.
"Let us unite ... and work towards a solid reconciliation," Sleiman said in his inaugural speech.
"I call upon all of you, politicians and citizens, to start a new phase called Lebanon and the Lebanese ... in order to achieve the interests of the nation.