Footage from the media conference on Thursday, showed Mr Tillerson sitting next to an empty chair waiting for several minutes for his counterpart Gebran Bassil to arrive.
When the foreign minister entered the room he greeted him cordially and the two shook hands. They then met with Mr Aoun.
It is standard diplomatic practice for all parties at official meets to walk into a room at the same time to generate a neutral and cooperative atmosphere.
Rafic Chlela, head of President Aoun’s media office, said Mr Tillerson had arrived a few minutes earlier than expected, and the meeting began on time.
The US Secretary of State is on a five-day regional tour taking in Lebanon as well as Egypt, Jordan, Kuwait and Turkey.
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“Mr President, thank you for the warm welcome and the open, frank, and productive discussion,” Mr Tillerson wrote in the Lebanese palace’s visitors book after the talks.
“The United States stands with the Lebanese people for a free and democratic Lebanon.”
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 almost two-year-long power vacuum.
Under Lebanon’s constitution, the president must be a Maronite Christian, the prime minister a Sunni Muslim, and the speaker of parliament a Shia Muslim.
Mr Tillerson also held meetings with speaker Nabih Berri and Prime Minister Saad Hariri.
Mr Aoun’s Christian party is a close political ally of Shia group Hezbollah, which is designated as a terrorist group by the US.
Hezbollah’s complicated role in Lebanon’s coalition government was highlighted last November when Mr Hariri dramatically resigned from his position on a visit to Riyadh. The decision was widely believed to have been orchestrated by his party’s Saudi backers with the long-term aim of weakening Hezbollah.
The militant group’s leader Hassan Nasrallah made several speeches calling on the country to unite and remain calm despite the heightened tensions, which many credited with preventing an outbreak of violence.
US President Donald Trump has been tough on Hezbollah, imposing new sanctions designed to damage Iran and its allies.
During his visit, Mr Tillerson made a rare admission that Hezbollah is an important political presence in Lebanon and that reality “must be recognised”.
However, in a news conference with Mr Hariri later on Thursday the Secretary of State warned that the group’s involvement in regional conflicts, such as Syria’s civil war, threatened Lebanon’s long-term stability.