The MP, who has twice visited Israel as part of LFI delegations, also criticised the expansion of Israeli settlements, saying that they “harm peace”.
He said “urgent and passionate” work was needed to secure security for Israelis and to “alleviate the suffering of the Palestinian people”.
Israeli and Palestinian advocates of a one-state solution were living in a “fantasy”, he added. “A one-state solution is simply not a solution at all. It would mean either the demise of Israel as a Jewish state or the demise of Israel as a democratic state.”
Mr Alexander said the threat posed by Iran must be taken seriously. The country’s funding of Hizbollah, support for Syria’s President Assad, and supply of weapons to the Taliban, meant “a nuclear armed Iran is not simply a threat to Israel, it is a threat to all nations”.
He added: “Israel has a right, indeed an obligation, to defend itself, and as past conflicts remind us, that demands a strong Israeli Defence Force.”
Israel’s ambassador to Britain Daniel Taub praised LFI, calling the group a “voice for clarity and honesty”.
Shadow Chancellor Ed Balls was among the Labour front bench MPs at the lunch — he is due to visit Israel this month.