Tillerson "reaffirmed to Berri the importance of the close U.S".
The YPG is the main component of the USA -backed Syrian Democratic Forces alliance that has seized vast territory from Islamic State in Syria.
"We try to be very precise in the actions we take to not harm the Lebanese people", he said during an interview with Al Hurra TV.
Tillerson is leaving Lebanon for Turkey.
"We hope the message reaches the White House", he added.More news: It looks like huge congratulations are in order for Amy Schumer
"We will preserve Lebanon's sovereignty in the face of Israel's aggression", Hariri said Monday. Lebanon says part of the wall follows the UN-demarcated "Blue Line" that was drawn up after Israel withdrew from southern Lebanon in 2000, and insists some sections will cut into its territory.
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.
He spoke Thursday at a joint press conference with Lebanese Prime Minister Saad Hariri, an ally of the West who is at odds with Hezbollah.
Hezbollah, which the United States deems a terrorist organization, has increased its military strength since the last major conflict with Israel in 2006.
Analysts are divided over the potential for U.S. Secretary of State Rex Tillerson's upcoming visit to Beirut to reap concrete results for Lebanon's oil and gas sector.More news: Crypto mining is slowing the search for ALIEN LIFE
"Mr President, thank you for the warm welcome and the open, frank, and productive discussion", Tillerson wrote in the Lebanese palace's visitors book after the talks.
Tillerson urged Lebanese leaders to uphold the country's commitment to staying out of regional conflicts.
The US has offered Lebanon mediation to ease tensions with Israel over the offshore gas fields in the Eastern Mediterranean.
Lebanon is also protesting Israeli violations of Israeli airspace, often to bomb targets inside neighboring Syria.
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.More news: Meek Mill Files Appeal Petition Over Cop's Alleged False Testimony
The long-standing border dispute between the two countries resurfaced recently as Lebanon invited foreign companies to sign exploration deals.