Washington is seeking a swift renewal of Israeli-Palestinian peace talks, as well as a comprehensive peace deal which draws in all nations in the region.
Michel Sleiman, the Lebanese president, has said Lebanon is ready to take party in any international peace conferences based on the Saudi-sponsored Arab peace initiative, promoted in 2002.
The proposal, backed by all 22 members of the Arab League, offers Israel normalisation of ties in return for a withdrawal from territory occupied in the 1967 war, a Palestinian state and an equitable solution to the Palestinian refugee problem.
Privately, though, Lebanese officials said they would inform Mitchell of Lebanon's opposition to naturalising some 400,000 Palestinian refugees living in the country, arguing that doing so would upset Lebanon's sectarian balance.
Most of the refugees, who make up 10 per cent of Lebanon's population, are Sunni Muslims.
This is the first time that Mitchell, who has Lebanese roots, has visited Lebanon in his visits to the region since he was appointed Middle East envoy in January.
Mitchell had been reluctant to visit Lebanon until after its parliamentary election, held last Sunday and billed as a battle between the ruling March 14 coalition and a Hezbollah-led alliance.
Ultimately, the US-backed March 14 alliance won the vote.
"These elections were an important milestone for this country. The United States remains steadfast in its support for a sovereign, free, and independent Lebanon," Mitchell said.
His visit to Lebanon comes just two days after he visited Israel and met Mahmoud Abbas, the Palestinian president, in Ramallah in the occupied West Bank, urging the two sides to move forward on a two-state solution.