US diplomat Frederic Hof had previously proposed a maritime demarcation line that would give Lebanon around two-thirds and Israel around one-third of a disputed triangular area of sea of around 860 square kilometres.
Parliament Speaker Nabih Berri told a US envoy on Friday that Lebanon rejects current proposals over the disputed marine borders with Israel, state media said.
Acting Assistant US Secretary of State David Satterfield also met Foreign Minister Gebran Bassil and Prime Minister Saad al Hariri on Friday.
"What is proposed is unacceptable," Lebanon's NNA cited Berri as saying in a meeting with Satterfield.
This was an apparent reference to a maritime demarcation line proposed by US diplomat Frederic Hof in 2012.
The line would give Lebanon around two-thirds and Israel around one-third of a disputed triangular area of sea of around 860 square kilometres (330 square miles).
A source in Berri's camp said Satterfield came with "a new plan ... after the American side became convinced" that Lebanon would not accept the Hof line.
It is unclear exactly what the new US suggestion to Lebanon regarding the disputed waters involves.
Berri insisted during the meeting with Satterfield that the maritime border should be drawn up through a tripartite committee that stemmed from a 1996 ceasefire, NNA said.
He said he wanted to see a similar process as produced the UN-demarcated Blue Line border between the two countries, which marks Israel's military withdrawal from southern Lebanon in 2000.