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.
"We support a free, democratic Lebanon free of influence of others, and we know that Lebanese Hezbollah is influenced by Iran". Tillerson is due to meet Lebanon's political leadership Thursday as part of a tour of the Middle East.
From 2006 until assuming his role in U.S. President Donald Trump's administration in 2016, Tillerson was ExxonMobil's chairman and CEO.
Progressive Socialist Party leader MP Walid Jumblat said on Thursday that President Michel Aoun has "given his remarks" to visiting U.S. secretary of state Rex Tillerson, noting that he sees "positivity" in Tillerson's statements.
Tillerson said Hezbollah's engagement in Syria has "perpetuated the bloodshed" in that country and threatens the security of Lebanon. Hezbollah, branded a "terrorist" organisation by the United States, is a key ally of Syrian President Bashar al-Assad and has fighters on the ground in the war-torn country supporting the regime. Commenting on the proposal, however, Aoun said that Lebanon will not give Israel a "millimeter".
Oxfam scandal: MSF fired 19 staff members over sexual misconduct in 2017
Oxfam's corporate partners, including Mark & Spencer, Heathrow Airport and Waterstones, are asking questions. The charity also led tributes to murdered MP and former Oxfam worker Jo Cox at the festival in 2016.
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 policy the three leaders wish to put forth is one hinging on the notion that Israel's actions along the southern and maritime border infringe upon Lebanon's rights.
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 long-standing dispute resurfaced recently as Lebanon invited companies to sign exploration deals.