The key issues refer to the tensions on the southern border due to the construction of a wall by Israel and the threats on oil and gas exploration projects in Block 9 at open seas, in jurisdictional waters that belong to Lebanon.
"Hebollah's entanglement in regional conflicts threatens the security of Lebanon", he added.
So far, the Lebanese government has rejected the US plan of sharing the offshore blocks, that was proposed by US Assistant Secretary of State David Sutterfield during his visit to Beirut last week.
Tillerson is in Lebanon, a major recipient of USA military aid, as part of a regional tour. "Their presence in Syria has perpetuated the bloodshed, increased the displacement of innocent people and propped up the barbaric Assad regime", Tillerson said at a news conference with Lebanese Prime Minister Saad Hariri.
Tillerson's visit, the first by a U.S. Secretary of State to Lebanon since 2014, got off to an awkward start as he waited several minutes in Baabda Palace for his meeting with President Michel Aoun, a Hezbollah ally.
"We will preserve Lebanon's sovereignty in the face of Israel's aggression", Hariri said Monday.
Tillerson urged Lebanese leaders to uphold the country's commitment to staying out of regional conflicts.
The long-standing border dispute between the two countries resurfaced recently as Lebanon invited foreign companies to sign exploration deals.
When asked about the maritime border dispute with Israel, including Lebanese media reports that Washington had asked Beirut to give up a portion of sea it claims, Tillerson denied the reports.
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.