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.
Resistance call
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.
"On this path to salvation, some valiant resistance and some courageous soldiers also offered their lives in order to defeat terrorism, Israeli aggression from south Lebanon to its north," he said.
"The achievements of the resistance should not be exploited in internal disputes."
James Bays, Al Jazeera's correspondent in Lebanon, said on Sunday that people were in a celebratory mood.
"Everyone from whatever background, from whatever political persuasion, whatever religious group has great expectations for this man. It might be hard for him to live up to them," he said.
'Crucial selection'
Rula Amin, Al Jazeera's correspondent in Beirut, said many Lebanese intellectuals said they would have preferred a civilian candidate, but many other observers believe the selection of Sleiman was crucial in order to end the country's political crisis.
Sleiman was elected Lebanon's president after
a deal was brokered in Qatar [AFP]
 She said: "It seems that for now both parties, both alliances have come to an agreement.
"The question on many people's mind is that is this a final settlement or just a truce?
"There are still many issues that need to be resolved. For this moment in Lebanon's history he is the best, fittest person to take the job."
Sleiman's election is part of a deal brokered on Wednesday in Doha, Qatar's capital, to end a political crisis that last month degenerated into violence.
Sixty-five people were killed when armed supporters of the Hezbollah-led opposition took control of much of Beirut after the government moved to outlaw the group's private communications network.
The clashes were the worst internal violence in Lebanon since the country's 1975-1990 civil war.
'Reconciliation wedding'
The Doha accord allows the opposition to have veto power on key policy decisions in a new cabinet of national unity.

But while it brought the country back from the brink of civil war, it failed to address many key issues, including Hezbollah's weapons stockpile.
Lebanon's presidency had been vacant since November, when Emile Lahoud stepped down at the end of his term with no elected successor because of political disputes.
Nineteen previous parliamentary sessions to formally elect a new president failed due to boycotts by the opposition.

Source: Al Jazeera and agencies