Aoun, who kept Tillerson waiting for several minutes at the palace ahead of their meeting, said he asked Tillerson to work on preventing what he said were ongoing Israeli violations of Lebanese sovereignty and said that Lebanon rejects Israeli claims over parts of the countries' maritime border.
Lebanese President Michel Aoun, an ally of Hezbollah, said Tillerson had listened and understood the Lebanese position regarding the border wall and maritime border dispute.
Monday's meeting, according to governmental sources, "looked into acting assistant USA secretary of state David Satterfield's proposal" to resolve a Lebanese-Israeli dispute over an 860-sq km maritime area. Lebanon says part of the wall follows the UN-demarcated "Blue Line" that was drawn up after Israel withdrew from southern Lebanon in 2000, and insists some sections will cut into its territory.
Tillerson said Hezbollah's engagement in Syria has "perpetuated the bloodshed" in that country and threatens the security of Lebanon.
Tillerson left the meeting with Aoun without making a statement, but he signed the guest book at the Baabda Presidential Palace.
The US Secretary of state is on a five-day regional tour taking in Lebanon as well as Egypt, Jordan, Kuwait and Turkey.
Tillerson's visit comes in the wake of Lebanon signing its first offshore oil and gas exploration agreements with an global consortium of energy companies, comprising France's Total, Italy's Eni and Russia's Novatek.
Israel regards Hezbollah as the biggest direct threat on its borders and has repeatedly struck it in Syria, where the group is fighting alongside President Bashar al-Assad in a civil war now entering its eighth year.
The visit comes amid a new USA effort to squeeze Iran with sanctions against Hezbollah and the Trump administration is hitting Hezbollah's financial network with new penalties as part of its efforts to limit Iran's influence throughout the region.
Israel claims that Lebanon will be drilling in areas owned by Israel.
Mr Aoun, a former army general, became president of Lebanon in October 2016, after a surprising shift in allegiances across the country's deeply divided political parties, ending an nearly two-year-long power vacuum.