"Preserving national unity and civil peace is a priority for us," Aoun told Pompeo, the Lebanese presidency said on its Twitter feed.
Pompeo met with Aoun at the presidential palace in Baabda, east of the capital Beirut on Friday.
The visiting top US diplomat claimed that his pressure on Iran and Hezbollah was working and urged Lebanon to stand up to the resistance movement which he accused of "terror and threats.” Presstv reported.
"Our pressure on Iran is simple. It's aimed at cutting off the funding for terrorists and it's working," he said in a statement after meeting Lebanese political leaders. "We believe that our work is already constraining Hezbollah's activities."
Earlier, the long-serving speaker of Lebanon's parliament, Nabih Berri, told Pompeo that American sanctions against Hezbollah were having a "negative impact on Lebanon and the Lebanese.”
Nabih Berri told the top US diplomat in a meeting in Beirut that Hezbollah is a Lebanese political party whose members are in the government and parliament, and that it is carrying out “resistance” against Israel to free Lebanese territory from Israeli occupation.
Earlier in the day, Pompeo also met with Lebanese Prime Minister Saad Hariri at the Grand Serail, which is the headquarters of the Prime Minister of Lebanon.