Tillerson's visit, part of a tour of the Middle East, comes at a time of tension between Lebanon and neighbouring Israel, notably over the role of Lebanese Shiite movement Hezbollah.
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.
Israeli Defense Minister Avigdor Lieberman described the exploration tender as " provocative" and suggested that Lebanon had put out invitations for bids from worldwide groups for a gas field "which is by all accounts ours".
Lebanon has vehemently denied those claims, arguing that the wall encroaches on Lebanese territory in 13 areas along the blue line which demarcated Israel's withdrawal from southern Lebanon in 2000, with Israel's recent incursions suggesting that it views the blue line as the definitive border between both sets of countries.
U.S. Secretary of State Rex Tillerson is urging Hezbollah to cease its activities overseas to help reduce tensions in the region.
US President Donald Trump has been tough on Hezbollah, imposing new sanctions created to damage Iran and its allies.
Lebanon's president says he has asked visiting U.S. Secretary of State Rex Tillerson to work on preventing ongoing Israeli violations of its sovereignty.
Tillerson said Hezbollah's engagement in Syria has "perpetuated the bloodshed" in that country and threatens the security of Lebanon.
It is a key ally of Syrian President Bashar al-Assad and has fighters on the ground in the war-torn country supporting the regime. Lebanon is upset about Israel's construction of a dividing wall along the border between the two countries, which are still technically at war.
Yet Lebanese officials have continuously rejected this proposal over the years, arguing that the totality of the 860-sq km falls under Lebanon's jurisdiction.
The visit comes amid a new US 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.
The long-standing maritime dispute resurfaced recently as Lebanon invited companies to sign exploration deals.
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