Aoun arrived in Riyadh yesterday night with a delegation of ministers.
It is his first trip to the kingdom since his election in November ended a two-year deadlock between Iran -- and Saudi -- backed blocs in the Lebanese parliament.
In an interview with Saudi state news channel Al-Ekhbaria, Aoun said his ministers of foreign affairs, education, finance and information would meet their counterparts "to find some fields of cooperation."
Aoun himself held talks over lunch on Tuesday with King Salman, but the official Saudi Press Agency gave no details of their content.
Analysts say Saudi Arabia is hoping for a more stable Lebanon, after concerns about the role played by Hezbollah in the Lebanese government.
The Iran-backed Shiite militant group has fighters in Syria supporting forces of President Bashar al-Assad.
Saudi Arabia, Iran's regional rival, backs some rebels opposed to Assad.
Riyadh last March declared Hezbollah a "terrorist organisation" and urged its citizens to leave Lebanon.
In February, the kingdom halted a USD 3 billion programme of military aid to Lebanon to protest what it said was "the stranglehold of Hezbollah on the state".
It aimed to ensure stability in a Lebanon weakened by internal divisions and threatened by jihadists.
Asked vaguely by Ekhbaria about the agreement, Aoun said: "Of course we will discuss all the possible issues."
Syria's nearly six-year civil war has been a major fault line in Lebanese politics, and the country hosts more than one million Syrian refugees.
Aoun told the Saudi channel that Lebanon's partners "have agreed to build Lebanon, regardless of the results in the other countries, because building Lebanon is for all, and secondly, security and stability is for all."
"The state must realise, and maintain, security and stability for individuals and groups even if there are different political visions regarding neighbouring and regional countries," Aoun said.
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