The neighbors have exchanged threats and condemnation over a border wall being constructed by Israel, a tender issued by Beirut for oil and gas exploration in disputed waters and arms flows to Lebanon's Iran-backed Hezbollah group.
Lebanese and Israeli officials said David Satterfield, acting assistant US secretary of state, was in Israel last week and in Lebanon this week on a mediation mission. US officials confirmed his travels without detailing his agenda.
"He (Satterfield) held talks regarding the (border) wall with Israel and said there is no call for concern, and there is no direction towards escalation," a senior Lebanese government official told Reuters on condition of anonymity.
"He assured the Lebanese that Israel does not want escalation."
An Israeli official, who also declined to be named, said Satterfield was "relaying messages" to Beirut about several matters of contention.
"Our position has always been that we do not want to see the situation inflamed," the official said, adding that at least two European countries were mediating, as well as the United States.
Meanwhile, Lebanese Cabinet Minister Pierre Abi Assi told reporters after a government meeting that top Lebanese officials are in contact with the United Nations and some countries that he did not name to try and decrease the tensions.
Abi Assi quoted Prime Minister Saad Hariri as telling the Cabinet that he, along with Aoun, the parliament speaker and the foreign minister are conducting the contacts and "we hope they will lead to positive results."
Hariri, according to Abi Assi, said Thursday that area in the water that Israel is claiming "is owned by Lebanon."
Lebanon has described Israel's border wall as an "aggression", saying it intrudes into Lebanese territory. Israel says the wall will be entirely on its side of the UN-recognized border.
On Thursday, Lebanese President Michel Aoun said talks were underway with friendly states "to prevent Israeli greed" and pledged to "confront any attack" on Lebanon's territory or waters, his office said.
Israel has also condemned Lebanon's oil and gas exploration tender as "very provocative," saying that one field, known as Block 9, juts into its waters. Lebanon says the block is entirely inside Lebanese waters.
Israel last went to war in Lebanon in 2006, against Hezbollah which, it says, has increased in strength since helping sway the Syrian civil war in President Bashar Assad's favor.
Israeli and US officials have said they believe Iran is setting up factories in Lebanon to make precision-guided missiles that may allow Hezbollah to threaten Israel's critical infrastructure in any future war. Israeli officials have hinted they could order preemptive strikes on such facilities.
Hezbollah and Iran have not responded to the missile allegations.
Satterfield is known to both Lebanon and Israel, as a former US ambassador to Beirut and former head of the international peacekeeping force in Egypt's Sinai desert, a role that put him in regular touch with Israeli security officials.
Asked about Satterfield's Lebanon visit, the spokesman for the US Embassy in Beirut said only that he came "to meet with government officials to discuss the US-Lebanon bilateral relationship."
Another US official told Reuters that Satterfield met Lebanese Prime Minister Saad al-Hariri on Tuesday.
His Beirut trip followed a visit to Tel Aviv last week to address a security conference. Israeli officials and the US Embassy in Israel declined to provide details on his talks with Prime Minister Benjamin Netanyahu's government.