Barak made the remarks after meeting Hosni Mubarak, the Egyptian president; Omar Suleiman, the intelligence chief; and Hussein Tantawi, the defence minister, in the Egyptian capital.
'Peace and security'
An Israeli official said Barak's visit aimed to look at ways to move forward following a speech by Binyamin Netanyahu, the Israeli prime minister, in which he applied heavy conditions for the establishment of any future Palestinian state.
"It is a really unique opportunity for the peace process because the common interest is so apparent"
Israeli defence minister
"He made it clear that the end result, the goal of the whole process is to have a situation where the two peoples, Palestinian and Israeli, are living side by side in two states in good neighbourliness, peace and security," Barak said.
"It is a really unique opportunity for the peace process because the common interest is so apparent regarding the struggle against hegemonic Iran, against radical terrorism, against proliferation of nuclear weapons."
Egypt has dismissed the speech as flawed, while the Palestinians have complained that it effectively rules out a sovereign Palestinian state.
Netanyahu said any two-state solution would first require international guarantees that the Palestinians would not be allowed army or control over their own borders and airspace.
He also ruled Palestinians being allowed to return to their lands inside what is now Israel and said that Jerusalem would remain undivided, dismissing Palestinian claims that the east of the city should be the capital of any future state.
Palestinian leaders have previously refused to recognise Israel as a Jewish state because they believe it weakens the position of the 20 per cent of Israel's citizens who are Arabs.
They also say it undermines the key demand for Palestinians refugees to return to the areas they left in 1948.
Mubarak has said that Israel's call to be recognised as a state for the Jewish people undermined efforts to achieve peace and has said he told Netanyahu, who visited Egypt last month, that peace talks should resume where they left off.
"The call to recognise Israel as a Jewish state complicates things further and scuppers the possibilities for peace," state news agency MENA quoted Mubarak as saying at a military ceremony.