The official SPA news agency said Salam spoke after meeting King Abdullah at Jeddah airport.
Earlier, after meeting Saudi Crown Prince Salman bin Abdulaziz, an adviser to Salam said his visit "is not related to the presidential election in Lebanon".
Hezbollah, one of Lebanon's two main blocs, is backed by Iran, Riyadh's Gulf rival.
The other is led by the son of assassinated former premier Rafiq Hariri, Saad Hariri who now lives in Saudi Arabia, a key backer of his bloc.
Hariri's Sunni-led bloc has backed a candidate Hezbollah has opposed without proposing an alternative.
In Jeddah, Salam met Hariri and said he "seemed serious in his efforts to reach a result that would enable... the election to take place".
The Lebanese parliament's latest attempt on Thursday to meet to vote on a new president failed for the fourth time, after the Hezbollah-led bloc boycotted the session leaving it without a quorum.
In December, Saudi Arabia pledged $3 billion for the Lebanese army to buy equipment from France.
Lebanon is sharply divided over the conflict in neighbouring Syria, where Hezbollah is fighting alongside Syrian troops.
Damascus dominated Lebanon for nearly 30 years until 2005, but still exerts significant influence there through Hezbollah, which is also a close ally of Iran.
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Earlier, after meeting Saudi Crown Prince Salman bin Abdulaziz, an adviser to Salam said his visit "is not related to the presidential election in Lebanon".
Hezbollah, one of Lebanon's two main blocs, is backed by Iran, Riyadh's Gulf rival.
The other is led by the son of assassinated former premier Rafiq Hariri, Saad Hariri who now lives in Saudi Arabia, a key backer of his bloc.
Hariri's Sunni-led bloc has backed a candidate Hezbollah has opposed without proposing an alternative.
In Jeddah, Salam met Hariri and said he "seemed serious in his efforts to reach a result that would enable... the election to take place".
The Lebanese parliament's latest attempt on Thursday to meet to vote on a new president failed for the fourth time, after the Hezbollah-led bloc boycotted the session leaving it without a quorum.
In December, Saudi Arabia pledged $3 billion for the Lebanese army to buy equipment from France.
Lebanon is sharply divided over the conflict in neighbouring Syria, where Hezbollah is fighting alongside Syrian troops.
Damascus dominated Lebanon for nearly 30 years until 2005, but still exerts significant influence there through Hezbollah, which is also a close ally of Iran.
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