Tillerson "reaffirmed to Berri the importance of the close U.S".
Israel has accused Iran of seeking to set up weapons factories in Lebanon, and the Israeli military last month said the country had turned into one "large missile factory".
Tillerson is leaving Lebanon for Turkey.
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President Michel Aoun made the comments during a meeting with Tillerson at the presidential palace on Thursday.
Tillerson urged Lebanese leaders to uphold the country's commitment to staying out of regional conflicts.
The visit coincides with heightened tensions between Lebanon and its southern neighbor over oil and gas reserves and Israel's construction of a border wall that Lebanon says encroaches on its territory.
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The Lebanese government will reject any U.S. proposals to resolve a border dispute with Israel, which will be formalized by U.S. Secretary of State Rex Tillerson during his visit to this capital, the Lebanese presidential office announced today.
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. Lebanese officials contest those claims, saying the area where it plans to drill belongs to Lebanon.
The tripartite meetings between Lebanon's three leaders also touched on Israel's construction of a 23-foot concrete wall along the blue line between the two countries, which Israel deems falls entirely on its side of the United Nations -recognized border.
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The U.S Secretary of State will also seek to discuss with Lebanese officials the Trump administration's intensified efforts to curtail Hezbollah's influence in the region, amid the introduction of amended legislation targetting the Iranian backed militant group's financial network that passed in October 2017.